I assume the OP wants to build some kind of system that will control an A/D converter and do something with the result... As Ron and AK have said, of course the FPGA can't do a conversion on its own, but could be interfaced to an A/D converter chip. You can get microcontrollers with built-in A/D converters but the same is not true (as far as I know) of FPGAs.
Funilly enough I'm just getting started in FPGA world myself - be warned, it's a *steep* learning curve, but very interesting. When I first started considering playing with one, nearly 10 years ago, the cost of development boards was prohibitive - but now there are some that are quite affordable.
Firstly, you'll need a development board. All FPGAs come in large surface mount packages that don't make for easy prototyping; they also need some support circuits like voltage regulators (often a few rails are required) and a configuration EEPROM.
The board that I have cost about £30 (GB pound) and has an Altera CycloneII FPGA - that's an old product now, but plenty capable for a beginner. It was purchaced through eBay, but via a friend so I'm afraid I can't tell you the name of the seller or exactly how it was listed. It also came with the JTAG/USB programming interface - you will need something like this, although many boards have this on-board meaning you simply plug in USB directly.
I believe (please correct me if I'm wrong here people!) that all the FPGA manufacturers provide a free version of their development tools. These are *massive* pieces of software (>5GB download) which you will need to install on your PC. I don't believe there are any "generic" tools for synthesis. Altera even do a version that runs under Linux - that's one of the main reasons I went for their product.
Regarding languages, yes, it's a choice between VHDL and Verilog. I chose VHDL (for some reason I can't recall any more), although I can currently barely say "hello world" in it. For this reason I'm having a go at designing as a schematic to get used to doing logic design.
Regarding development boards, Lattice do some very small and cheap ones which may be of interest. The Altera baord I have is an "unoffical" Chinese product and, although mine works perfectly, you may get better support with a vendor's own official board and programmer.
If you let us know where in the world you are/what suppilers you have access to, perhaps someone can recomend a particular product for you to buy?
**EDIT**
PS. As AK said, do you have a particular task you need to do or is it for the joy of leaning? If the former, then perhaps soneone can suggest the most direct route to achieving it.