1. Above all else, play for fun and enjoy the game. Improve at any pace you feel comfortable with
2. Gradually get familiar with all the cards you're playing with. If you want to do it casual way, just play games. If you want to do it pro way, in addition go to wiki.dominionstrategy.com and read articles on the cards. With practice, you'll get a hang of which card is good or bad in which circumstances.
3. While playing - before your first turn, analyze the board you're facing. Search for key components (+cards, +action, +buy, trashing, attacks...) and try to see how they synergize with each other. Among other things, this is something that Adam Horton videos () are great to learn from - as he usually talks about the board for a minute or two before he starts playing. It's ever educational to see how better players than you think and analyze the board
When you analyzed the board, formulate a strategy and stick with it through the game (which doesn't mean that you should be inflexible and not adapt to what your opponent is doing). If you won, it means your strategy had at least some merit (though of course you should always try to improve). If you lost, see where you went wrong. Maybe your strategy was inferior; maybe it was good but your execution was suboptimal. Whatever the case is, try to learn from yours and your opponent's mistake and get better for the next game.
4. As always, watching records of top players is quite a good way to improve your game. I myself have mostly watched WW's youtube channel (), but there are tons of other great ones as well.
5. Have fun playing (this can't be emphasized enough)