At their core, tire load indexes and speed ratings work under the same principle: the higher the number/letter, the higher the load the tire can carry, and the higher the speed it can reach, save for an H, which appears in the middle the speed chart.
A load index of 71, for example, has a load capacity of 761 pounds, while a 110 load index indicates a load capacity of 2,337 pounds; this is per tire, not for all four combined. To see if the tires support a load, simply find the load capacity of the individual tires and add them all together.
Speed is much simpler, requiring just a chart. The letter on the tire corresponds to a specific threshold, from 75 mph for an L, to 186 for a Y. For specific letters, it is best to consult a chart, which can be found in numerous locations on the Internet. Tirerack.com offers a simple, no nonsense chart, as do most tire sales websites.
The reason why an H appears out of order in the chart is due to the older, outdated system, which simply offered speed ranges using an S, H or V. Since 1991, a more thorough labeling system has been used with thresholds rather than ranges.