Most contracts in the UK require you to find your own way to and from the 'site'. Some agencies will provide local information regarding travel and I have been offered maps and directions by the well organized agencies.
If Europe or further field is your destination then you will normally be provided with a flight there and back, at the start and end of the contract. However, if the contract is ongoing, and you manage some free time you are normally expected to make your own travel arrangements if home beckons, but again, every situation is different. Having worked on a few winter contracts in Frankfurt we were all provided with free flights half way through the 6 month contract back to our nearest home airport.
As for Europe I would recommend taking your own car as it's great to get out and about and see the local sites. It's easy using ferries or the Chunnel and if you have never drove abroad its all part of the adventure. On this note though, make sure you get adequate insurance cover for your car. Most insurance companies provide what is called 'Green Card Cover' for Europe only up to 30 days. You will be expected to pay for any further cover over this period. Some agencies will provide travel expenses up to the cost of an airline ticket if you make your own way to the site.
Another good tip is, when you are settled into your new digs, find a local mobile phone shop and get a local sim card for the mobile phone. This will save a lot of money on phone calls and you normally can buy them over the counter. You may have to provide details of your local address and show your passport.
I treat all the travel as part of the job. It is a bit of a nomadic life style, moving from job to job and living out of a suitcase but it gets in your blood! If you don't like traveling and never knowing where you might be working next week then maybe contracting isn't for you !