Gambia is very easy to get to from Europe. There are chartered and scheduled flights from the UK operated by Thomas Cook, Monarch and SN Brussels airways (via Brussels).
There are a number of package tour operators to choose from, but The Gambia Experience is probably the best as they have a long relationship with Gambia and use excellent hotels. They also promote respectful and sustainable tourism and contribute money to local projects.
If want a little more say in the timing and accomodation for your visit you could buy a 'flight only' (either chartered to save money or scheduled for more comfort and flexibility) and book your accommodation separately. There are many hotels and B&Bs to choose from.
If you want to book a taxi before you go, to transfer you from the airport, you can do that at http://www.airporttransfer.gm/.