What are the best practices for gathering preflight weather and information?
At least in the US there are plenty of ways to get a flight briefing.
My usual sources of pre-flight information are, roughly in order:


The Weather Channel
No kidding, if I'm planning a long/multi-day trip I'll start looking at the long-range forecasts 10 days before my flight using The Weather Channel's iPhone app or their website.
As far as weather information goes it's pretty decent (which means "frequently wrong up until 24 hours before go-time, but still worth paying attention to").
Charts (VFR or IFR), Airport Diagrams, and the A/FD
If you're planning more than a hop around the local pattern you should familiarize yourself with the airspace you'll be passing through, landmarks (and obstacles) on the ground, and navaid / airport frequencies. Charts and other FAA publications provide a great way to do that, and you can also usually pick up a phone and call the airport you're flying to for additional information.
All of this documentation is available in a variety of forms - Paper, electronic downloads direct from the FAA (as linked above), or as part of flight-planning software like Foreflight, Garmin Pilot, WingX Pro, etc.
The National Weather Service
A few days before a planned flight it's worth reading the forecaster's discussion to see how confident the people predicting the weather are about their guesses. This is also something you should check the day of departure if there's any uncertainty about the weather.
Electronic briefing tools (DUAT/DUATS/Foreflight/etc.)
About 24 hours out you can get official briefings from DUAT/DUATS/Foreflight and a bunch of other flight planning tools. Get them and learn to read them.  


  Electronic briefings from many of these tools are recorded and count as an "official briefing" - a record is made that you requested and received the information. You are responsible for understanding all the information that just got dumped in your lap however, and that's a huge responsibility, especially for a student pilot!

Flight Service Briefings (1-800-WX-BRIEF)
The day of departure your final briefing should be a phone call to flight service to speak with an actual briefer to review your flight. If you can sit down and have your electronic briefing from #3 in front of you it's very helpful because you can follow along with the briefer to be sure you didn't miss anything.


  Calls to Flight Service are recorded and count as an official briefing. If you're unclear on anything you're being told you can ask for clarification.





Of all the tools available I personally think the best one is calling flight service and speaking to a briefer. If your instructor has never made you do this I'd say they're skipping out on a critical bit of your training, and you owe it to yourself to pick up the phone and .

This is your big chance to talk to a live human being and ask any questions - big ones that I always ask are "Are there any TFRs along my route of flight?", and if I'm anywhere near a restricted area I'll check its status ("Is R-12345 active?").