Holding a heading is a lot more accurate if you remember to set the DG against the magnetic compass before departure. You'll want to periodically check to be sure the DG hasn't precessed as you fly along. On a student cross-country flight I had to hold a 45-degree wind correction angle to stay on track from Morristown, New Jersey, to Harrisburg, Pennsylvania. I couldn't figure out why the wind was so much different than forecast and from what I expected from the preflight planning. It wasn't until I got ready to make the return flight that I realized I'd never set - or checked - the DG against the compass before and on the flight out. I learned that lesson.
A cross-country flight using radio (VOR) navigation requires that you fly from VOR to VOR, having calculated the wind correction angle for each segment of the flight. It's a good tactic to be particularly vigilant and fly a couple hundred feet off the required VFR hemispheric-rule altitude (odd thousands plus 500 for headings of 000 to 179 degrees and even thousands plus 500 for headings of 180 to 359 degrees) when you're crossing a VOR because there may be others using the VOR for guidance.
It's important to be sure that everything you need is handy in the cockpit. You'll want to have pencils, pens or china markers accessible for jotting down AWOS/ASOS or ATIS information. Sectionals should be within easy reach (I number the top of the charts in the order I need them so I'm not distracted trying to figure out which chart comes next). An E6-B or calculator, a plotter or ruler, batteries for your headset or flashlight should all be within easy reach. If you've got advanced avionics onboard you might want to keep the "quick reference" cards nearby.
Today, cross-country navigation has changed - dramatically. The revolution began with RNAVs (area navigation) that allowed you to create a course by "electronically" creating virtual VORs along a straight-line route and continued with GPS navigators and moving maps. But Murphy's Law (if anything can go wrong, it will) applies, so relying on your GPS can be a mistake.
On the other hand, if you have a GPS there's nothing wrong with using it to back up your flight planning. The GPS will confirm your groundspeed calculations and your estimate of how long it will take you to get to your destination.
Once you're under way there are four things you have to constantly assess: whether you're on course; whether the weather (winds and clouds) is doing what was forecast; whether there are other airplanes trying to occupy your airspace; and whether you still have enough fuel to reach your destination. You can get help avoiding other airplanes by asking for flight following. If their work load permits, air traffic controllers will provide traffic advisories. It doesn't eliminate your requirement to "see and avoid." Watching for traffic, you want to be careful not to fixate and continue to scan in small segments of the sky. If traffic appears on the horizon and doesn't seem to be moving it means - unless something changes - you're on a collision course. Whenever traffic is called by a controller, I always look in the direction advised. If I don't see the traffic quickly, I'll look to the other side of the sky, just in case the controller's gotten his directions confused (it happens). If I do see the called traffic, I'll still look in the other direction to make sure no one's sneaking up on me while I'm distracted by the called traffic I'm watching.
You've taken care of the course with your flight planning and proficient pilotage and radio navigation. From your calculations you know what the winds are doing and the weather should be obvious to you by looking out the windscreen. If you have any questions about what the weather's doing ahead, you can monitor or call Flight Watch (EFAS or En Route Flight Advisory Service) on 122.0. Flight Watch is designed to provide pilots - who have already received a preflight weather briefing - with weather advisories that apply to their route and altitude. The service is available over the continental United States from 5,000 agl to 17,500 msl, but is accessible at lower altitudes within reach of a ground station. When you call it's important to indicate where you are in relation to a nearby VOR so the closest Flight Watch station can respond. After explaining what you need and getting a response, it's good practice to give a pirep (pilot report) about the conditions you're experiencing, cloud cover, temperature and winds. That way other pilots will have the advantage of your observations. Using the sectional you can also monitor the automatic weather reporting stations (AWOS/ASOS/ATIS) that are within range. If you're concerned about a strong crosswind at your destination, sampling the reports of nearby airports may help you find one where the wind is blowing closer to straight down the runway. Nothing wrong with changing a destination if it seems prudent. Discretion is always better than trying to prove your valor.