For the IP address, open a command prompt (Windows 2K or XP) or DOS prompt (Windows 98) window (for and type ipconfig. Your IP address will be listed. (The address may change from time to time if you are using DHCP from your Linksys.)
Start and End are probably the starting and ending port range in case you need to open up a while range like from port 5000 to port 5019. Easier than entering 20 of them (especially since most of those little routers only give you room for like ten rules max). For a single port you can probably just put the number in start and leave end blank or put the same number in both.
Application is just anything you want to call it for a shorthand. The router uses only numbers. The shorthand is for you to remember why you put that in.
TCP & UDP: How much time do you have? (Seriously.) Short answer: They are different methods (protocols) for sending data across the internet. Different games use different protocols, and the game you are trying to open the ports for should mention which protocol each of those ports need to be open for. Many games use only TCP or only UDP. Some use both, but might run TCP on 5121 and UDP on 6900. You just need to match what the game needs.
Case: Enermax CS-A106USB
P/S: OCZ OCZ700GXSSLI 700W
Motherboard: ASUS P5N32-E SLI
CPU: Intel E6300(idle 35C/load 39C)
RAM: OCZ Platinum Rev 2 DDR2 800 MHz (4 x 1GB) 4-4-4-15-T1 (2.1v)
Hard Disk: Seagate 2x250GB SATA ST3250620AS in RAID1
Monitor: Mitsubishi DP900u
Graphics: BFG GeForce 8800GT PCI-E
Sound: SoundBlaster X-Fi Fatal1ty
Speakers: Klipsch ProMedia v.2-400 4.1 speakers
Optical: LiteOn 16X DVD-ROM; Sony DRU-710A DVD-RW