There are a lot of ways to become a better Boggle player besides just playing Boggle (although playing Boggle is certainly the most effective method!). A lot of the activities that you probably already enjoy doing if you're a Boggle fan will help improve your Boggle playing over time. All I can recommend is to continue to do the following Boggle-friendly activities.
Reading is one of the best methods to raise your Boggle skill level. Read anything and everything you want! The act of reading will help you play Boggle better by simply exposing you to more words. It's not just that reading helps you learn new words. It also places lots of words in front of your eyes that you may already know, but reading brings these words up closer to the front of your mind. This will make the words more accessible in the Boggle word cache in your brain.
In addition, reading will help in Boggle because it makes you think and analyze in a way that other media do not. To improve your Boggle play, read fiction, nonfiction, newspapers, magazines, billboards, whatever strikes your fancy!
Word and puzzle games are also a great way to change the way you think, and make you a better Boggle player. Doing crossword puzzles, in particular, is an underrated activity that forces your brain to play with letters in much the same way that Boggle does. While many people seem to think that crossword puzzles are only for grandparents, or that they're just too difficult, crossword puzzles are actually a lot of fun once you start doing them. And, just like Boggle, there's a pretty high learning curve.
Scrabble, although not in the same league as Boggle if you ask me, can be enjoyable and help to improve your Boggle skill. Just as in Boggle, Scrabble requires that you create words out of a limited number of letters. Playing Scrabble will increase your Boggle success.
Finally, if you're up for a totally new activity which will, aside from being satisfying and educational, also help your Boggle playing, try learning a second language. The analytic skills necessary to understanding and learning a new language are similar to what is needed to play Boggle. And learning languages is cool and fun!