The answer is, like most, it depends. Rather than just give you rules to memorize, I will show you the logic behind the rules. Understanding the thought process will help you for those situations where none of the rules fit quite exactly, or to decide when to break the rules.
Goals
The most important thing to remember about Standard American bidding is that you are trying to find out if your side has game, in particular 4 of a major or 3NT. So the two questions you are trying to answer are, does your side have a combined 26 points? Does you side have an 8 card fit in a major? You want to find out the answer to these questions as quickly as possible.
All of the below situations assume that you have support for your partner's suit and have your own suit to bid.
When Your Partner Opens a Minor
If your partner opens a minor suit (1C or 1D) and you have support for that minor, and you also have a major, bid your major suit. Even if you only have 4 cards in your major and you have 5 or more cards in your partner's minor. Until you have ruled out game in the major, look for a major fit rather than a minor fit.
For example, if you have:
S 10 5
H K J 4 2
D A 8 6 4 3
C 4 3
and your partner opens 1D, you should bid 1H. Yes, diamonds is almost definitely your best fit, but you first need to explore to see if your side can make 4 hearts, which will probably be easier to make than 5 diamonds, if your partner has four card heart support for you. If your partner does anything other than support your hearts, you can now bid diamonds with a clear conscience.
When Your Partner Opens a Major
If your partner opens a major (1H or 1S) and you have support for that major and another suit, its a little bit more complicated. I'll break this down by point ranges.
0-5 Points
Pass. You know you have less than game, so don't encourage your partner. Of course, if the opponents enter the bidding, you may bid later, knowing you've already told your partner you have a weak hand. (This, of course, is also true if they had opened a minor.)
6-10 Points
Bid 2 of your partner's suit. Even if your other suit is really nice, support partner. Given your weakness, it increases the odds that the opponents will bid something. Now you are in a competitive auction, and your partner doesn't know about the fit, and so can't make an informed decision. And by the time the bidding gets around to you, the level might be too high for you to be comfortable bidding again.
S A Q 10 7 5
H 6 4 2
D 6 4 3
C 4 3This is really important, so I'm going to repeat it. If you have a weak hand, the most important thing you can do, is to support your partner's major suit bid. On the above hand, if your partner opens 1H, bid 2H, not 1S.
10-12 Points
This is an in-between scenario. In some systems, like 2/1 (a popular system based on Standard American), it would depend on whether you have 4 card support for your partner's major or only 3. For the HSBC standard, I'm going to recommend going the simpler route of just bidding 3 of your partner's major. This bid shows your strength range and your support all at once. It's very descriptive, makes it hard for the opponents to enter the bidding, and hopefully gives your partner enough information to do the right thing.
13+ Points
With this strong hand, you already have both the questions answered. You know your side has 26+ points and you know your side has an 8 card major fit. Now you have the freedom to consider other options. Maybe your side has slam (6 or 7). Bid your suit and see what happens. A new suit by you is forcing, so you aren't worried about your partner passing. You can always bid 4 of your partner's major as your next bid, if nothing good comes about.
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