Some of us receive training from our universities, though that seems to be rarer these days. There are also some excellent online resources available for learning paleography, which is just a fancy word for the study of old writing. For instance, if you are interested in early modern (about 1500-1700) English handwriting, I would thoroughly recommend this website, which has information on alphabets, transcription conventions, and also course lessons, which give you an opportunity to practice your skills using photo reproductions of manuscripts from Cambridge:

https://www.english.cam.ac.uk/ceres/ehoc/

Really, though, the only way to learn to read old handwriting well is a lot of practice with it. The first time I went to an archive as a graduate student, I almost started crying because of how difficult it was to read the manuscript I had called up. But by the end of the week, I could (very slowly) make sense of it. It's a bit of a puzzle--there are certain abbreviations and letter-sound combinations that you become familiar with. The best example is probably the now obsolete letter called a thorn, which usually looks like a "y." The thorn stood for a "th" sound: so for instance, ye=the. Once you pick up on these kinds of tricks, it becomes easier and easier to read.

One helpful thing is to make yourself a "key"--basically, a detailed notebook.

You're already recognizing some words, which is great. Let's say you're able to recognize the word "the." Start a section for the letter "t" and copy the way your writer makes a "t." Do the same for "h," and so on. With those letters, you'll be in a position to recognize "that," "there," and add new letters. Be prepared for a writer to have different variants of the same letter.

It sounds like playing a game of hangman, as you go letter by letter, but you will start to fill things in, and later you can go back to the key for ideas when you run into a tricky passage.