Obtain Cobweb

You can only acquire Cobwebs by breaking them with Shears. Even a silk touch tool will not work. Shears can be crafted from 2 iron ingots. You can reroll a Sherpherd (loom) villager who will trade 2 emeralds for shears. Remember that it is impossible for the Snowy village shepherd house to generate due to a typo.

Minshafts are very common in the overworld and they very commonly have cobwebs throughout the structure. You can find a Minshaft using endar for a chest minecart, and also see here and here for how to find Minshafts quickly. 

In Badlands biomes, you can find Minshafts on the surface, so looking out for seeing Dark Oak or rails can be good in these biomes for finding cobwebs. 

If you are entering without shears, there is a 22.48% chance you get 2 iron from a single chest minecart (i.e. the one you found with endar). Else, there is usually plenty of iron ore you can use instead. 

Igloo basements always generate with exactly 1 cobweb, in the top corner. Usually, you will be going to the igloo earlygame for other goals, and will not have the iron for shears. 

If that is the case, you should not necessarily tunnel vision on going back to the igloo if your line took you elsewhere afterwards. Mineshafts and Trial Chambers are still very strong for other reasons. It is very unlikely you get enough string for a loom and 2 emeralds, but you could possibly trade with the villager for shears. 

Overall, a Trial Chamber has roughly a 50% chance to have at least 1 cobweb, but even if you whiff you can try to force it.

If you have a husk or zombie spawner, you will not have a spider spawner. There is a 33.3% that your Trial Chamber has a spider spawner. Look out for which type your melee spawner is. 

A silverfish, slime or baby zombie spawner means you have no cave spider spawner. Note that the baby zombie spawner has non-mossy cobblestone too, differentiating it from the zombie one. You have a 25% chance that your Trial Chamber has a cave spider spawner. 

If you don't have a Spider or Cave Spider spawner, you can still try to get a cobweb through Weaving using an Ominous Trial. You will need to get an Ominous Bottle in order to do this.

Weaving is a 14.29% pick for a Trial Spawner, and you will need to wait 8 seconds after activating the spawner to see which projectile effect was chosen. This choice is location based, meaning two very close spawners are likely to choose the same effect. Once you get weaving, killing a mob who has the effect should generate 2-3 cobwebs around where they died. 

A mob with weaving will have dark Weakness-like potion swirl particles as well as white cobweb particles coming off them. 

If you see any of the following effects after triggering an Ominous Trial Spawner, you did not get Weaving:

Poison and Slowness come from the arrows, which are rolled separately from the lingering effects. Getting either of those does not indicate a failed Weaving attempt. 

98.77% of strongholds will have at least 1 library, and 96.98% have both (simulated by ClearColdWater). It is therefore highly likely that you will have at least 1 cobweb in a stronghold if you choose to send it. This is a very snipeable goal and end lines are somewhat weaker in the meta now, but it is still a consistent option.  

2% of villages are abandoned, meaning that no Iron Golem spawns, Villagers are replaced with Zombie Villagers, and blocks are replaced, some into Cobwebs. 

You can usually spot an abandoned village if you can see it, usually because of the Cobwebs themselves. If you don't see the village however, you can use the entity pie chart to see if you have any villagers in your render distance. You can also check for iron golem to confirm, but remember that 50% of Taiga villages will not have Golems, even if they're not abandoned. 

Since there's no golem, it might not actually be that easy to get the shears needed to obtain the cobweb. Bear this in mind if you were planning to send this goal early. 

The Spider Spawner room in Woodland Mansions will generate with cobwebs, but it is a secret room and not necessarily the easiest to locate. It can generate on any floor and because it is secret, you will need to break a wall in order to get in. 

Mansions are not very common, but they can provide alternatives to a lot of different goals. Bear this in mind when building a line.