From either the coordinates we've provided for a car park, or the turn onto "Terrible Mountain Road" a little further up, follow that road up to the ruins of the old Fairview Mine at 12,000 ft. Even if you have 4WD, we would recommend parking here just to keep things sporting. The road to here is okay. Beyond the mine, the old roadbed follows a wide ridge on the eastern flank of "Terrible Mountain" until it comes to the base of Fairview Peak. As it follows this wide ridge, it only gains a modest amount of elevation. From the base of Fairview, a trail heads directly up the south ridge, initially through/on tundra which higher up gives way to broken talus. The cairn-marked trail continues through the talus to the summit.
In 2009, when we arrived at the summit, we found a small, stone building that looked recently occupied or used, but which had a large snowdrift inside. Apparently, according to Marianne Curtis, efforts are underway to "restore" this building. Built in 1912, it was originally a fire tower lookout, but was struck by lightening so many times, it was abandoned. A second story wood structure has been added above the first floor stone now. See our photo gallery for a view provided by Marianne of this building.
Once you've reached this summit, return as you came. The entire hike may only take 2 - 3 hours, so if you're looking for another summit the same day, take FR765 to the top of Cumberland Pass and Napoleon Peak (a 12er) and Fitzpatrick can also be completed in short enough order to still avoid the afternoon showers.
Links to other information, routes & trip reports for this peak that may be helpful.