Here I offer my best advice for getting strong at bughouse. Beginning players who follow this advice always gain points over time.
#1 Don't fear early sacrifices
If you focus on development, creating space around your King, and moving quickly, you won't get mated very often. (Sometimes your partner will give two Knights, a Rook, Bishop, and Queen. Bughouse is unfair and unjust by nature). Let's survey some of the usual sacrifices.
1.
2.
2.1.
2.2.
White is fine. White's partner has a lot of material to work with, which should be worth more than one Queen.
3.
3.1
Ke2, avoiding pawn checks, is best. Your partner should not have given a Queen.
If you move both e and d pawns, it is very hard to get mated due to a sacrifice. Generally, when someone gets mated early, it is because they didn't move their e and d pawns, which means the King has nowhere to move to.
A pawn or Bishop mates White here. This would be easily avoided if White had moved the e pawn.
#2 Don't play early sacrifices
Paul Morphy famously said "help your pieces help you". To adopt this for bughouse, help your pieces help the pieces your partner gets for you. This helps you help your team.
And just as in ordinary chess, a good sacrifice is prepared by strong positional play. Let's look at three sample game with some good positional moves.
1.
2.
3.
Unless your opponent has committed some huge oversight, such as allowing Bxf7+ without moving e and d pawns, the sacrifice is likely to be unwarranted. If early sacrifices worked reliably, bughouse would not work as a game. It would be a race to sacrifice a Knight of f7 first, and would be more like tic-tac-toe than chess.
Many beginners think that they are the first to come up Bxf7+ or Nxf7. And if you happen to partner such a player, perhaps the most appropriate response is to be pragmatic and try to feed them, in order to win. But it is extremely difficult to win reliably, which is what you should be aspiring for.
You also lose out a lot of interesting and deep positions in these sorts of games. "Ok, we sit it down, and hope I can get you two knights and two pawns (or whatever) in six seconds." It is not a chess move, but it is important: be the kind of partner you would want to have yourself. If you want a partner to feed you, try being the sort of player who feeds your partner. You will see that it is not easy to whip up a Knight and Queen in 5 moves. Everyone wants a partner who is flexible, who can get trades quickly, but who never asks for material that is hard to get, capable of attacking, and capable of defense. Be like the partner you want to have.
A good sacrifice does not depend on particular pieces in the short term, but it is reasonable to sacrifice and then ask for trades in general, over many moves. For example...
Trades are good for White at almost every point, but never essential.
#3 Give up the Queen to avoid passivity
You misplayed the opening maybe. And you're getting pushed around the board a bit, leading to something like this.
Black should probably just play Na6 here, giving up the Queen. If Black saves the Queen, Black loses too much time. White doesn't need much material to demolish Black. If you give up your Queen, do it on your partner's move, and get a little material back for the Queen. It is better than losing a Rook for nothing. Even if you are losing material, give your partner something to work with. Even if you are close to being mated, you should grab as much material as you can for your partner. Sometimes you can prevent your opponent from mating you in 2 or 3 by threatening to take a piece that your partner can use to deliver mate in 1.
#4 Play fast
I assume that you understand the importance of remaining ahead on time of your partner's opponent. In order to play fast, you should know some opening theory. In order to know opening theory, you should watch the streams. HelmsKnight and JannLeeCrazyhouse are the best two for bughouse streams. But you don't need to only watch 2700-2800 strength players. Even watching players around the 2100-2200 is a good way to learn--providing those players are self-critical and always looking for better moves.
There are some patterns that you should see at a glance. Take smothered mates, for instance...
White can win by dropping a Rook or Queen on g8, then dropping a Knight at f7. The Bishop on d5 means that Black has to capture the heavy with the Rook, leading to the smothered mate.
Here, White can exploit the pin on the g7 pawn to do the same thing. N@h6+, then R@g8, then Nxf7#.
When IM Caspiwins partnered me, he gave the following checkmate on my board. (I would never have found this by myself).
Two Knights mate. N@h3, gxh3, N@f3, Kh1, and Nxf2.
#5 Bring out your partner's strengths
A strong bughouse player makes their partner stronger. Sometimes, this is a stylistic issue, such as trading low, or trading high. A great opening for trading low is the following.
If your partner is a titled player, playing against a bughouse specialist, this can be very effective. Depriving the bughouse specialist of piece drops favors the chess master or grandmaster, who will be better at maneuvering existing pieces.
If your partner likes to grab material early and then get safe, this is also a good way to go.
As far as trading high, I'm not sure there is any particularly good opening for forcing that. Lines with 1.e4 e5 tend towards higher trades.
Part of it is more psychological than anything else. The best partners are encouraging, make you feel relaxed, and can suffer reversals with equanimity. (I never said I was one of the best partners). In seriousness, everyone wants to win and no-one is completely immune from getting annoyed or stressed. (There is losing a good game and losing because your partner didn't move their e pawn and was mated in 9 moves by a pawn). But one should in general avoid getting too sassy with such players.
Communication is key. For that, I recommend voice. You probably gain 100 elo points in strength by being on voice with a partner. Instead of having to click "no queen", one can simply say it without losing any time moving the mouse. You can communicate more nuanced plans even without sits on both boards.
Conclusion
Much more could be said. Maybe I will write something for more intermediate players. But if you are 1500 and you read this entire post, congratulations. I wish you success in achieving 2000.