A little known service outside of the maritime world is the RadioFax system. Operated by your tax dollars, NOAA creates weather charts that you can get via your web browser, email, or short wave radio (with some additional gear). Charts cover most of the world and are available as a look at "now", a 24, 48, and even 96 hour forecast.
Reading the charts takes a little practice, but it's not hard. Importantly for a mariner, they contain information you actually need such as storm tracks, wind speed, and developing storms. There are some guides as to what the various symbols mean, and NOAA has its own guide as well which although fairly technical is certainly all encompassing. In a nutshell the tighter the lines, and anything with an "L" in the middle of it is a bad thing. The little hockey sticks indicate wind strength and speed. Each long blade on the stick equals 10 knots, a small one 5 knots. So two long sticks and a short one are 25 knots.
NOAA is even nice enough to put "GALE", "STORM", and some other handy labels on there. "DVLPG" means "developing", so obviously "DVLPG STORM" is less wonderful news than "DSIPT STORM" which means "dissipating".
I'll let you have some fun exploring the weather charts that are available to you. The next time you hear a forecast say that there is a storm approaching, grab a weather chart and see if you can identify it on the map. It's a lot easier to do than you'd think, and you'll begin to learn what the different symbols mean.
For my particular area, I access the North East Pacific Surface charts. I can also simply send the below text in an email to firstname.lastname@example.org, and get back three charts. One is the current conditions, another is 48 hours out, and the last one 96 hours out (the legend in the top right tells you which is which). Just send this in the body of an email to that email address above, and wait a minute. Make sure you check your spam folder: