Interesting Deus Ex bug

[WarLocke]

or is it you gain points until you have enough to upgrade a skill?

That's it exactly. You gain experience for accomplishing certain goals, and you spend it on the skills of your choice. You'll get a good amount for simply accomplishing your objectives, but you can gain much more from bonuses. Often if you find an out-of-the-way nook or cranny you'll get an "exploration" bonus. Sometimes you get a "critical location" bonus (seems to be earned by entering a plot-necessary location by unusual means, I think). The experience for these bonuses usually isn't all that much (25, 50, and a couple 100/150s later on), but if you explore thoroughly, they do add up.

As an example, I'm fairly sure I'm nearing the end of the game, but I have two skills at Master (Rifles and Computer, easily 8500exp each in total), Low-Tech at Advanced (4015exp), and three skills at Trained (Lockpicking, Electronics, Swimming -- 1800, 1800, and 675exp). Not even counting unspent experience (and my bugged Pistols skill), I've earned in excess of 25,000 experience over the course of the game.