This page will provide a fairly simplified introduction to overcalls. It explicitly excludes balancing overcalls and jump shift overcalls (that is another topic).
Note that others may have different descriptions. What matters is that you and your partner try to adhere to the guidelines described here. You work as a team.
I cannot provide for every single scenario. You would do better by using logic instead of rote.
Definition:
The one who overcalled is the "intervenor"
The partner of the intervenor is the "advancer".
At 1 level : 8-16HCP (8-9HCP for "aggressive overcalls")
At 2 level : 10-16HCP (10-11 HCP for "aggressive overcalls")
At 3 level (e.g. to overcall a weak 2 opener by opponents): Around 16+ points (including distribution points) and a good suit (preferably 6+).
We won't discuss 3 level overcalls further in this page.
You might ask "What if I have 17 or more HCP"? Then you make a takeout double, intending to bid at least once more regardless of what partner bids. Partner will recognize that you are a strong hand once he sees you rebidding (normal takeouts do not result in intervenor rebidding unless it is to raise advancer's suit). This topic is out of scope of this page, and should be dealt with under takeout doubles.
It is too easy to be aggressive. The problem with aggressive overcalls is that
Partner may mistake your strength and overbid.
Opponents take information from your bidding and upgrade their hand. Especially if your partner raises your bid (showing that you and partner have most of that suit).
Opponents let you play and penalize you.
Partner may lead to your suit, when another lead might be better.
I suggest that you are aggressive when more than one of the following conditions are satisfied. Do not always think that an aggressive overcall is always a good thing to do. Very frequently, it is better to defend without giving opponents information.
You have an Ace in the suit (partner will lead to you)
You have a shapely hand (5-5, 5-4, void or singleton in opponents suit etc).
Your partner had already passed (showing he doesn't have an opening hand)
You are non-vul.
When you overcall, partner should assume you overcalled non-aggressive when deciding whether to bid on or not. i.e. assume that you overcalled with 10+ HCP at 1 level or 12+ HCP at 2 level.
Revision for constructive bidding. i.e. good chance of making contract using points.
2 level trump contract : at least 7 cd fit (yes! 5-2 fit is ok) and 18+ points (including DP).
3 level trump contract : 8+ cd fit and 21+ points (including DP).
4 level trump contract: 8+ cd fit (9 preferred) and 26+ points (including DP).
1NT : 18+ HCP (if balanced. count extra for 5+ cd suits)
2NT: 22+ HCP (if balanced. count extra for 5+ cd suits)
3NT : 26+ HCP (if balanced. count extra for 5+ cd suits)
When I say "constructive bidding", it means you should take into account your partner's points and your points in deciding what to do. Please assume that your partner has 10HCP when he overcalls at 1 level and 12 HCP when he overcalls at 2 level (i.e. assume he made a non-aggressive overcall with a minimum).
Raise or limit raise partner's suit.
With <7 pts or so, use LOTT and raise as high as possible.
With 7-10 pts or so, bid constructively. Your partner has 10 HCP or 12 HCP. You should be able to support a single raise. If you have 4 cd support, consider reserving a further raise, using LOTT as a guide.
With 10+ points, cuebid limit raise. Partner responds constructively assuming you have 10 pts.
You should bid constructively or just pass. Remember your partner has 10HCP or 12HCP.
Example:
with good stops in opponents suit, bid 1NT after intervenor overcalls 1 level with 8-11HCP, 2NT with 12-14HCP etc. If intervenor overcalls with a 2 level overcall, adjust accordingly.
If you have 0-1 cds in your partner's suit and a good 5+ cds of your own and around "overcall strength", consider bidding your 5+ cd suit at the cheapest level. You are "taking over the overcall". With a good opening hand, jump a level or constructively bid 2NT/3NT (with stops in opponent's suit).
Note that you should be able to play at 2 level with a 5-2 fit. Do not panic and try to change suit if your partner overcalls in that suit and you have only 2 cds.