When you go out to dance you will soon find out that most people at a Milonga will follow some form of etiquette. Some of these conventions are nigh-universal, others are local.As a follower
The subjects people are most worried about are generally along these lines:
How long to dance with a person
One convention that seems to be valid everywhere is that you generally dance to the end of a tanda with a person. A tanda can consist of three or four songs, so if you don't want to dance all four songs with the person you intend to ask, you would normally ask them on the second song of the current tanda. If you are at a milonga where the DJ doesn't structure music by tandas the general agreement seems to be that you dance a minimum of three songs together.
Only if a person has a tremendously uncomfortable embrace, terrible BO, behaves in an unenjoyable way or does something else that you find unacceptable would you normally stop dancing with them after the first song (or even leave them mid-song). In some places dropping a dancer after just one or two songs will reflect badly on them and might mean that others will hesitate to ask her or him thereafter - hence use sparingly.
In Europe it is not uncommon that two dancers who enjoy dancing together will dance together for as long as they like. When in a traditional milonga in Buenos Aires, however, consider carefully if you really want to ask a person to dance for a second consecutive tanda - traditionally this means you would also like to take them home for the night. If you would like to dance with that dancer for longer, but don't want to imply other interests, just take a break and ask them again after a few tandas have passed. In the US there seems to be a habit whereby people who don't know each other dance a tanda or two, but not necessarily more.
The end of your dance encounter is normally heralded by a 'thank you'...make sure that you don't inadvertently shorten a lovely dance by saying 'thank you' just because you've enjoyed yourself. Most tango dancers will assume that you have just told them you don't want to dance with them any longer and will generally return the thank you and walk off.
Asking somebody to dance
Depending on where you are in the world there are a lot of different ideas how best to ask another person to dance. The traditional Porteño way is to use the cabeceo, but in Europe and the US it is equally common to walk up to somebody and ask verbally. Interestingly it is still not at all a matter of course that women ask men verbally just as much as men ask women. Some men seem to enjoy being approached, whilst others are quietly traumatized and will earmark the woman who has asked them to be put on their personal blacklist. In that sense (and some people claim in many others as well) the cabeceo is very good for women, because it allows them to be more self-determined in finding a dance partner.
If you are at a milonga and can't quite figure out how people ask each other to dance don't hesitate to ask the organizer or any other friendly-looking person.
Even if you know how to, asking other people to dance can still be a minefield. Agreeing to dance with somebody is, of course, a free choice, and - unpleasant as it is to be rejected - it should be clear that we all have the right to reject a dance without having to give a reason or be apologetic about it.
No matter whether the cabeceo is used or not, people tend to show via body language if they want to be asked to dance. If e.g. you approach a person and they persistently look into another direction or keep rummaging in their bag up to the moment when you're standing in front of them it is likely that they don't feel like dancing with you right then, right there. Likewise, a person who wears no shoes has probably decided to have a break (if you like to slip out of your shoes, though, note that sitting around shoeless in the milonga is frowned upon in Buenos Aires - as is changing shoes at the table).
Sometimes people sit around the dance floor and chat. If they are chatting whilst waiting for the next dance you can normally observe that they are still looking around trying to catch other dancers eyes - if they don't look up from their chat when you stand in front of them, you will likely not get a dance out of them even if you interrupt. Don't put them on your blacklist forever when they say 'no'...you might have a splendid time dancing with them at the next milonga/practica/in a few hours/etc.
If somebody tells you that they don't want to dance 'right now' don't sit down right next to them to wait it out. Go away and ask somebody else - don't ask the person right next to them, though! Nobody is flattered by being the second choice and most people will decline.
Think about who you ask and then dance accordingly. If you are a relatively inexperienced dancer that doesn't mean you can't ask somebody who is very experienced. You can - but if they have said yes, maybe don't ask them for that second tanda. Don't ask them to correct you or to show you something new either.
If you are a relatively experienced dancer and you like to ask beginners: don't inflict that leg-wrap/boleo/piernazo/desplazamiento on them that you've just learned last week and shove them into position if they don't get it. Do the stuff they already know and enjoy.
Saying no to an offer to dance
There are different ways to reject a person who didn't read the signs right - whatever you choose to say, say it in a friendly manner. Fair or not, egos are easily bruised - so keep in mind that people talk about their experiences and that the tango scene is small. If you are snooty, unfriendly or don't do what you say it will inevitably get around and might well spoil your chances of dancing with people you would like to dance with.
If you decline a dance by saying that you are resting, that you don't like the music, that you need to go to the bathroom, that you need to cool down, etc. you might still raise the expectation that you will be available for dancing at some later stage. If you leave the door open in this way, make sure you stick to what you have said you would do. You might also say 'no thanks, not now, but I will find you later.'
If you are sure you don't want to dance with the person in question just smile at them in a friendly way and say 'No, but thank you very much for asking' - or something to that effect.
Saying 'no' to one person just to get up to dance two seconds later when somebody more desirable has come along is an absolute no-no. Declining a dance-offer means committing yourself to sitting out at least until the song is over (if not for another song or two). If the leader/follower of your dreams asks you after you have refused someone else's offer, that's just tough. Explain to them that you can't dance with them right now, but would love to do so for the next tanda.
A milonga is a neither a class nor a practica
Another convention which people universally agree (but don't always act) upon is that you don't teach at the Milonga. A dance evening is for fun and dancing, not for lecturing or asking others for technique tips. The 'no-teaching-at the-milonga'-rule is one which is worth respecting, or else you may find that some dancers will reward comments on their technique with a curt 'thank you' and a brisk walk off the dance floor. For the more experienced dancers who dance with a beginner it might of course be tempting to volunteer some advice, especially if the beginners asks...but just save that for the Practica and try meanwhile to quietly check your own technique for possible flaws.
Just to digress: at the Practica you may find still, though, that not everybody is keen to hear advice, no matter how well-meaning it may be. So, before you start correcting others, think about what you could correct in yourself to make things work better. If in doubt, ask your partner what they can feel - and once you've done all this without being able to solve the problem start thinking about what your partner could change.
It probably goes without saying that it is nice to be clean at the start of the milonga. Being clean at the end of the milonga, though, is an unrealistic goal if one also wants to dance a lot. There are, however, measures to make one's sweatiness a little more bearable to others. Firstly, use anti-perspirant or deodorant. Consider, though, that some people suffer from intolerance to perfumes and aftershaves, so don't douse yourself in your favourite scent, or these dancers might not be able to dance with you. Other people might object to smelling like you for the rest of the night and will decline to dance with you for that reason.
If you use make-up, keep in mind that it is likely to come off when you sweat...or when you are in contact with a sweating surface. Those who wear light colours might object to your foundation, eye shadow or lipstick on their shirt.
Tango dancers are by and large extremely tolerant to the sweat of strangers, but if you sweat profusely take some time to dry off between dances, or bring a set of clothes to change into. You can also bring a flannel to wipe your brow. Smaller people generally don't like being dripped on while dancing, and the taller ones might find your sweat makes their eyes burn.
If you're a man, shave well in advance. Stubble can cause nasty rash on the followers' cheeks and noses, while bloody cuts might keep them well away altogether. If your stubble is there to stay, make sure that you don't press your face against that of your follower, unless she insists.
La Ronda - the line of dance
Last but not least there are rules how to dance together. Remember that you are not alone, dancing with just one partner. You are dancing with many other couples in front, behind and next to you.
Depending on the size of the dancefloor and the popularity of the milonga you could be dancing with some 100 other couples...
Dancing as if everybody else is your enemy is no fun - but dancing surrounded by friends is actually great.
If you step onto the dancefloor try to make eye contact with the leader you step in front of, so that s/he is aware you're coming. If more than half the song is over consider waiting for the next gap between songs before you get onto the floor.
A dancefloor is often subdivided into lanes - make a decision which lane you are going to dance in and stick to it. Don't cross the middle, but dance in as big a circle as possible. Overtaking creates chaos because you need to change from one lane into the other, therefore overtake only if it is absolutely necessary - i.e. not just because the leader in front of you is a tiny fraction too slow for your taste. Reasons to overtake can be that
As a leader
Injuries inflicted by pointy tango heels can be nasty and painful - they can disrupt another person's enjoyable dance experience, or even worse, their evening.