I haven’t played bridge in ages, but that might actually give me some good perspective to step back and give some advice. So, three points (and actual experts, feel free to correct this very old and maybe incorrectly-remembered advice):
(1) The main thing to think about, philosophically, is that each bid you make is sort of a “yes, and…” on top of previous bids you’ve made. So, for instance, if you open 1H, you’re promising 13+ points and 5+ hearts. If you then bid 2H on your next bid, whatever your partner responds with, you’re never just saying “hey, remember, I have hearts” or “no, I don’t like that idea, I still have 13 points and 5 hearts”. You must be providing MORE info than your previous bids did. There are way way too many combinations of bids to begin to cover all the rules for what the “yes, and…” actually means. But generally, bidding a suit again means “oh, and I have more of that suit than I previously said”. And jumping a level higher than necessary means “oh, and I have a more powerful hand than I had previously promised”. So 1H - 1NT - 2H, the second bid of 2H is now promising 6+ hearts, rather than just the 5+ already promised.
Keeping that in mind, there are two primary sub-conversations that are always going on, and the bidding is designed to answer both of these questions for both players as fast as possible:
(2) Do we, between the two of us, have an 8-card major suit?
and even more importantly
(3) Do we, between the two of us, have the approximately 26ish high card points necessary to make a game in a major suit or NT? If not, we wan to stop our bidding as soon as possible in a non-catastrophic contract. If so, we want to find that game bid.
(3) in particular explains why the precise high card point ranges of the bids are important. If your partner opens 1H, they are promising 13+ HCP, but, to be more precise, they are promising something like 13-20 HCP, because with 21+ they would open something stronger (2C is often an artificial bid that means “I have a super strong hand”, but says nothing about suits). So if your partner opens 1H, and you have 3HCP, then the max HCP you can have, as a partnership, is 23. So you can not make a game. That’s why it’s OK for you to pass there, but not if you have 6+ HCP, Because if you have 6+ HCP, and your partner has the strongest possible 1H opening, and you pass, then they will never get a chance to make a “yes, and” bid saying they have 20 HCP, and you will fail to make your game.
But this works both ways. Let’s say that your bidding agreement is that if you can’t support your partner’s suit, you bid 1NT if you have 6-9 HCP. Then, once you have made that bid, if you are doing it honestly, your partner (who of course knows how many HCP they have) now has a very precise idea of the total HCP between both your hands. And they can now pass or keep bidding.
Basically, you are never allowed to pass short of game until you “know” that game is not possible, due to a bid with a “cap” from your partner plus your own hand.
The other important thing to do is find 8-card majors. Most of the time, an 8-card suit will be either 4-4 or 5-3 between your two hands. That’s why 5-cards-major-openings is such a useful convention… it immediate plants a staff and says not just “hmm, I’m kinda interested in hearts”, but “I have FIVE of the hearts we need”. And, because 5-card-majors are so important, opening up 1C or 1D also clearly and strongly says “I do NOT have a 5-card-major, period”. At which point, partner, if they don’t have at least a 4-card-major, immediately knows that no 5-card-major is possible. So, for major suits, any bid of the major suit makes a promise of length. And (generally speaking) any time you could have bit a major suit but did not is a denial of length.
For instance:
1C - 2C
Opener is denying a 5-card major
Responder is denying a 4-card major
At this point, after two bids, both partners know that they have no major suit contract
1C - 1H - 1NT
Opener has denied a 5-card major
Responder has promised 4+ hearts
Opener has denied exactly 4 hearts (and, probably, denied 4 spades as well, as they skipped their chance to go 1C - 1H - 1S, which would VERY clearly describe their hand, and thus would be a good bid to make)
So, they might still have 8 hearts between them. If responder has exactly 4 hearts only, then THEY know they don’t have 8 hearts, but original-opener doesn’t, yet. etc.