Gauntleds in FS1 are SP extra missions while FS2 ones are MP-Coop.
Anyway you fly as single ship (unlimited ship/weapon choice). You encounter single weak fighter, then 2 of em, next time 1 average, 2, 3, 1 strong, 2, 3, 1 very strong, 2, 3, 4 weak, 4 average, 4 strong, 4 very strong (after this first stage is complete and you may return to base OR if you are playing as bomber continue). 2nd stage contains one cruiser with 2 fighter escort (several waves). After destroying cruiser there's 3rd stage with destroyer and 4 fighter escort (several waves). After that gauntled is complete.
There are 3 gauntleds in standard FS. In Inferno there should be 5 (Terran, Vasudan, SOC, EA and Shivan).
Gauntleds are made for training. It's "How far will you get in?"-like mode. When you fly fighter you easily complete first stage and 2nd with little trouble, but you're unable to complete third (or able if you're flying Vesuvius with Assassin bombs

). When you're flying bomber it would be hard to complete first, but second and third will be easier.