A simple rule of thumb for staggered starts on a track is that each solid-line-stagger after the start represents the stagger for one turn. So, for example, if you are on a 400 meter outdoor track and want to run 200 meters, whichever lane you are in, start at the first solid-line stagger in that lane. If you want to run 400 meters, start at the second solid-line stagger, etc.
Penn State's outdoor track is a 400m track with 48 inch lanes, but has some mile markings as well. On the inside curb before the common finish line, there are 4 equally spaced white arrows that indicate the additional distance needed to run quarter miles up to a mile in lane 1 . To run a quarter-mile, back up to the first arrow and run to the common finish plus one lap. For a half-mile, back up to the second arrow and run to the common finish plus two laps, etc.
There are also some mile markings on the outside unnumbered "warmup" lane. Quarter miles are marked in white on the outside curb from 1/4 to 3 miles. You'll need to count laps to get this right. The 1/4-mile mark is about 60 yards before the common finish line. To run a 1/4-mile in the marked warmup lane, start at the common finish and run counterclockwise to the 1/4-mile mark, 6/7 of a lap. To run a mile in the marked warmup lane, start at the common finish line, run three full laps, then run to the 1-mile mark, for a total of about 3.4 laps.
For an excellent and more complete explanation of track markings, see this site.
This site has a fine online distance calculator to help you figure out how much you've run in any lane for any size track.