The most obvious thing is to run more. The law of specificity is for real. Although you can get some carry over effect from other activities, there really is no substitute for running. However, distance/speed does matter, a lot. Training for a better 50m sprint is VERY different than training for a 50 mile run.
Improving sprinting: This typically involves low volume sprinting with long rest breaks, plus some strength training and plyometrics. Too much volume will result in the conversion of type IIx fibers to the slower IIa fibers, no good for sprinters.
For all distances over 1 mile I tend to use only 3 tools: (use the zone #s on the left, not the right)
Tool 1: Easy pace running (MAF pace or zone 2 pace) Most elite athletes spend about 80% of their training volume in this zone. Training in this zone improves leg durability, improves economy, and increases the speed at the fuel crossover point (you burn more fat at faster speeds). It can also push up lactate threshold a little and even have a small impact on VO2 max in novices.
Tool 2: Threshold Pace (10K race pace or zone 4). This pace does a good job of pushing up the lactate threshold. It can increase your critical speed (the speed that you can hold for an extended period of time). A big dose of threshold is 40 minutes (i.e., 2 X 20 min), a small dose is 5 minutes. I would not use threshold intervals more than once per week.
Tool 3: VO2 max intervals (zone 5, max sustainable pace for 4-6 minutes, or 1 mile race pace). This pace is great for driving up the VO2 max. It is a powerful stimulus for aerobic adaptation and just a little is plenty. A big dose is 10-12 minutes, but 5-6 minutes is adequate. I would not do more than two VO2 max interval sessions per week.
If we put the tools together in a periodized program we would do something like:
Phase 1: Nothing but Tool 1 paced running. Slowly increase volume/mileage over time during this phase (10% increase per week rule). This phase should last as long as you are able. Training adaptations in this phase don't plateau for a long, long time.
Phase 2: Tool 1, and one to two Tool 2 workouts. The type of fitness we get from tool 2 tends to plateau after 8 weeks or so. As a result, phase 2 should last about 2 months.
Phase 3: Tool 1, Tool 2 and one (maybe two for experienced athletes) Tool 3 workouts. Tool 3 fitness plateaus after 3-6 weeks, so phase 3 should last 6 weeks max.
Following phase 3, you take a short taper and then have the race of your life ! ; )
That is a generic periodized program. We would adjust significantly for different race distances. For example, an ultra-marathoner should simply stay in Phase 1, with only sporadic Tool 2 workouts.