Buy one of the ASVAB prep books and study it cover to cover. Take practice tests online, military.com has some practice tests. Study your basic algebra, geometry and trig. The two math sections, the reading and the word knowledge sections are what make your AFQT score which is the score that qualifies you for entering the Coast Guard so be sure to do well on those sections especially, it is scored from 1 to 99. Take a look at all of the different sections on the test and see which one is your weakest and just the basics of that particular subject.
Don't worry too much about the ASVAB, I'm 5 years out of high school and only studied my basic algebra in my car before I went in to take the test and I still did great. Everything on the test is very basic and pretty much at a high school level of knowledge. I struggle most with the auto and shop information simply because I don't have any experience in those areas. Good luck and remember to take your time and read each question carefully!