Quick first impression - both players here have a lot to work on.
First thing to learn. Piece values. Generally speaking, a queen is worth more than a rook, which is worth more than a bishop/knight (those 2 are about the same), which is worth more than a pawn. Q > R > B = N > P. Both sides start with equal material (the same forces) and if you can make advantageous trades, it becomes easier (but not guaranteed) to win later.
I don't like the idea of putting numbers to their worth, but for a beginner the values Q=10, R=5, B=N=3.5, P=1 may help. (The common value of 3 for a B/N can lure beginners into thinking B+N = R+P, which it is decidedly not.) Try not to assign significance to these values too much, it's purely a crutch to help you take your first steps in chess.
Then we can see major mistakes. 7. Be3? is a blunder, losing your bishop on c4 for but a pawn. (Annotation: question marks behind a move indicate bad moves.) 15. Rf1? loses the knight on e5 for nothing. 17. Nxc7+? loses a knight for a pawn. 20. Qxd8+? loses a queen for a rook. All these trades lose you material - avoid making such moves. This is probably the single most important thing to learn at this stage. In fact, stronger players would consider the position after 7...bxc4 to already be losing for white. Instead, 7. Bb3 would have preserved your bishop.
Nonetheless, beginners often slip up like that, so don't just give up there. Black's play after that was still very bad, not moving his pieces off the back rank for a long while. Notice how after 11. Nd5 your king is safe and your pieces look active, while black's are almost comically lazy? This is an advantage in development - white should have good chances despite being a piece down. Always remember to try to get all your pieces active at the start, like you did here.
Next: Look out for chances to win material. Not losing material on your part is one thing, but look for opportunities to take what your opponent gives you. 13. Rxe5+ would have forked the opponent's king and bishop; black cannot defend, e.g. 13. Rxe5+ Ne7 (trying to protect the bishop) 14. Nxe7 (or 14. Rxe7+, but not 14. Rxf5? Nxf5 as the knight becomes unpinned) wins you a piece.
14. Nc6+ is a discovered check from the rook on e1, while your knight attacks black's queen. Black will lose his queen for a knight here; 14. Nc6+ Qe7? 15. Ncxe7 doesn't help him and just plain drops a queen for nothing.
14...Re6 was not very dangerous (although black was already up from 7...bxc4 earlier.) The e5-knight is defended by the e1-rook. Black's only threat was ...c6 to exploit the pin on the d-file, but something simple like 15. Rad1 would have defended against that.
Instead of 17. Nxc7+?, try 17. Rxe5+ Nxe5 18. Re1 where black's e5-knight is pinned and the g5-pawn becomes fragile too if the queen tries to defend.
There is no mate in 1 or 2 after 21...Nd4. White is dead lost, yes, but there's no quick mate. Chess is not checkers - captures are not compulsory. After 22...Bd3? you should have taken 23. cxd4, although you're still too far behind in material to even draw. (22...Bd3? 23. cxd4 Qe2 24. Ra1 Qxb2 25. Rd1 etc - black cannot force a quick mate but there's no doubt about the victor.)
The above points are most important. Don't lose material, and keep an eye out for simple tactics that let you win material.
Once you've learnt to not drop pieces outright, consider this: black's 2...f6? is not good because of 3. Nxe5 fxe5? (3...Qe7 is the better option) 4. Qh5+ g6 5. Qxe5+ and the rook on h8 dies. A well-known inferior line for black.
Hey there! I've been playing around on this site for a few days, and it's gotten me really interested in chess. I'm obviously at a disadvantage in most of my games due to a lack of experience, and I've only won once. But I keep up the effort, and I'm enjoying myself. I could use a little help. I feel like I'm playing well, but sometimes it feels like I'm just moving pieces without any real plan. I lose a lot of material and I end up getting out-planned. Here's a match I played about an hour ago:
I'm still new, so I'm probably missing a lot of the basic strategy, but any help would be greatly appreciated.