Start with something simple like SHA256D used in Bitcoin:

https://github.com/progranism/Open-Source-FPGA-Bitcoin-Miner

Or something from the official Xilinx marketing publication:

http://issuu.com/xcelljournal/docs/xcell_journal_issue_84/16

Have fun!

Edit: I forgot to include standard explanation about the difference between CPU programming and FPGA programming.

CPUs have von Neumann architecture with linear memory, e.g. from 0 to 4294967296. Compiling and running your first 10 line program will take seconds on your typical usable computer with 4GB of RAM.

FPGA have a completely generic two dimensional architecture that literally has kajilion of constraints. Most of those constraints are secret to the FPGA vendor. The XCVU9P FPGA discussed in this thread has about 2104 pads, just describing the pads that are actually connected with useful signals on the VCU1525 board is a file that has 25 pages in the manual. Those are the constraints that are visible and not secret.

When compiling your first 10 line FPGA program the Xilinx toolchain will still have to process those constraints even if you use less than 1% of 1% of the whole VCU9P chip. On the other hand the small XC7A35T chip on the training board has much, much less internal constraints that needs to be read by the toolchain.

You will observe that your small 10 line FPGA program will be completely compiled and done for a small device like like 7A35T while for the large device the Xilinx toolchain is still decrypting the secret VU9P constraints file. Amazon recommends that you run their FPGA development kit for VCU9P on a computer with 32GB of RAM to get sensible performance for nontrivial programs.

Just be aware of the above.

Edit2: Trying to learn logic design on a high-end device may seriously test your patience. Start with a low-end device.

Edit3: Grammar fixes.