There are a few types of runs that make up most training plans. The first I'll discuss is speedwork. As the name implies, speedwork involves running really fast. Different people have different ideas of what exactly constitutes speedwork. I'm going with a simple definition:
Any run where talking is extremely difficult.
Speedwork helps make you faster. There aren't too many times you'll need speed in ultras, especially your first. I recommend speedwork to prevent you from getting slower over time. Long-term ultrarunners that only run long, slow distances usually experience a degree of muscle atrophy and loss of speed. Occasionally running fast helps prevent that.
Speedwork can take several forms. Some people like running repeats, or laps around a track. Others like to do tempo runs, which are shorter, faster runs. I prefer running short races, like 5ks or add a sprinting component to my crosstraining. I'm not a huge fan of fast running, so I've used some various “motivational” methods over the years.
My favorite method involved sprinting down sand hills. It was easy, fun, and made me feel really fast.
The worst method involved an evil workout called a Tabata. It involved sprinting for 30 seconds, walking for 20, then repeating that cycle eight times. I'd rest for a few seconds, then do it again. I repeated the eight cycles six times. I threw up twice. It wouldn't have been so bad if it weren't for the Taco Bell spicy burrito I ate a few hours before.