Inquisitors fight depending on what you give him. If you read the DH codex, you'll find that he can be accompanied with 'henchmen' (retinue) that can boost his abilities, depending on who you field and how many. Some example lists:
Assaulty Inq.
Inq. Lord w/ daemonhammer, bolt pistol, & Halocaust Spell
w/ retinue of 3 acolytes (w/ storm shields) and 3 warriors (combat servitors. they come w/ power fists and CCW)
this list is a tad pricey, (220 altogether, or 300 if you add a chimera to it) but it can potentially kick ass in CC. 6-9 power fists and 4-5 thunder hammer strikes are very likely gonna kill stuff, and the acolytes can hand out invul saves to power attacks.
Shooty Inq.
Inquisitor (elite selection) w/ Psycannon
w/ retinue of 2 sages, 1 mystic, and 3 warriors (all gun servitors with heavy bolters.)
This list is 150 pts, but it shall work very well against hordes or tau (ap4). (add 25 pts if you want him to be an Inq. Lord)
There's one other thing about Inquisitors. If you have an Inq. Lord, you can get an assassin too. they are expensive and specialize in one particular thing, but they do it quite well. But, i'll that for the codex to explain.