Of course, if you have money to spend, there is no point in reading this. I used to be a poor college student and now I'm a broke college student, so I'm usually on the hunt for good deals and will (sometimes) sacrifice quality and comfort for a few quid or euro. But either way, I've been there, and you may have not. So here's some musings on my experiences:

Trains: Trains, I think, are the best way to travel within a country. I've taken the train several times from London and Edinburgh up to Leuchars, travelling either on GNER or Scotrail. Train travel is (usually) much more relaxing and much less stressful than plane travel, and if you're travelling short distances and within a country, the security is nonexistent. (This really isn't to say I haven't felt safe. I've never felt unsafe on a train.) And besides this, you get to see things up close, like the countryside:

Now, the train to Paris is a little bit of a different story, since immigration and security are a must. I was patted down on the way to Paris (I always seem to set the thing off), but immigration wasn't terrible. From London Waterloo, I took the Eurostar to Gare de Nord, and slept the whole way since my train was at 5:30 AM one way and 6:30 AM the other.

Baggage can also be a little more of a hassle on the train, since you have to deal with it yourself. When my family came to visit over my Easter holiday, we had 6 people with 5 big bags, and it took all of us and some tight-space maneuvering to get the luggage on and off. Overall, though, I think trains are the way to go, if you can use them.

Planes: Unfortunately, you can't (usually) take a train over the ocean or the sea, so I flew to Dublin this past weekend. I flew Ryanair, which was possibly the most efficient airline ever. It also cost me 30 pounds, which is somewhere around 50 dollars (I try not to calculate it, it makes me sad), for my roundtrip ticket. Going into Dublin Airport I had to go through immigration, but not coming out. I still don't understand the immigration laws for the European Union although I am taking a class on citizenship this semester. Security is a big deal in Edinburgh, and there are signs up on the wall about flying near bird flu-infected areas. I was patted down again in Edinburgh.

Getting to and from the airport can sometimes be a hassle, especially if you live in a small town like I do. I took a train from Leuchars to Haymarket in Edinburgh, and then the airport express bus. From Dublin airport I took a city bus to my hotel. It seems that a trip never has just one or two legs of travel; I'm always getting on and off buses and trains and in and out of taxis only to get on and off of a plane.

As far as cheap airlines go, Europe is apparently the place for them. There's Ryanair and Easyjet, Jet2 and BMI, and I'm sure a host of other ones. All are booked almost exclusively online. However, the airfare that is posted is deceiving, and often doesn't include taxes and fees, which can run up to probably 40 pounds sometimes.

Hotels: I've stayed in a number of hotels this semester, but no hostels. I've had two "worst hotel ever" experiences, one in Aberdeen and one in Paris, but mostly I've had really good experiences. Overall, I recommend Expedia.com for hotel bookings, although good deals can be found on lastminute.com. If it's a deal you're looking for, and you don't mind public transportation, it might be worth it to look for a hotel a little out of the way. For example, my hotel in Dublin, the Jurys Croke Park, was outside of the city centre by about a mile, but it was a gorgeous hotel for only 100 dollars a night.

General Advice:
Get a guidebook. There are plenty to choose from; I recommend the "Let's Go" or Fodor's series.
If you have a lot to see and not a lot of time, use one of the hop on/hop off city bus tours.
If you're in a city, have a lot of time and not a lot to see, get out of the city for a day. Trish and I went to Howth for a day, outside of Dublin, just by taking the commuter train. We went on a cliff walk and sat by the ocean and had an overall relaxing day outside of the grime and bustle of Dublin.
Make sure you rest! If you sightsee all day and never get back to your hotel for a nap or never sit down for a real lunch, you won't get to experience the nightlife, which (at least for the younger set) can be the most interesting.

I'll leave off with some advice from a friend who was in London last semester. Before I came here, we had this conversation:
"So, as far as travelling goes, any advice?"
"Do a lot of it!"