For obvious reasons, you need to know what the weather will be like when and where you fly your cross-country trip. Fortunately, the FAA and the National Weather Service (NWS) have you covered.
There are flight service stations (FSS) throughout the country that you can call to get the latest weather information for anywhere in the country. The FSSs are supplemented with computerized weather and related flight services called DUATS (Direct User Access Terminal System). You also can call for a weather briefing at 1-800-WX-BRIEF (992-7433).
What type of weather information do you need? Because you're a VFR (visual flight rules) pilot you need to know if your flight will meet VFR visibility minimums. In fact, you should have personal flight minimums that are more conservative than regulations require, at least until you get more flying experience. As you gather weather information, remember that a weather report tells you what has happened or is happening, and a weather forecast tells you what (probably) will happen.
Winds are also important weather information. Note that the direction and velocity of winds could be different at ground elevation than it is at flight altitude, called winds aloft.
For your knowledge test you will need to know some weather codes, even though many reports and forecasts don't use these codes any more. Hopefully, future tests will change this. Meantime, your ground school instructor or course will teach you what codes you'll need for the knowledge test.
Your instructor won't sign you off for a solo cross-country trip until he or she is comfortable that you 1) are not flying into a weather problem, and 2) have the skills to handle probable weather changes. Remember, too, that the FSS or weather briefer will help you even more if you identify yourself as a student pilot planning your first cross-country solo. They're there to help you, not test you.