Normally I use specialists in the early game when my cities hit a population cap through happiness. Then I use them again in the late game when my cities start getting big enough to use all of their tiles...with one city with a lot of specialists for GP.
However, you can use specialists throughout the game in a variety of ways.
1) Make your specialists pay their bills. For example, with representation and the sistine chapel, all of your specialist give you a free +2 culture and +3 beakers. Suddenly, they become a lot more attractive.
2) Turn commerce cities into production ones for brief times. The one problem with commerce cities is the lack of hammers, which give them all their cool multiplers. However, you can use engineers and priests to give them some hammers for a time to let them finish these buildings quicker.
3) Focus your civilization in "emergency times." Lets say your in a race with another civ to get Liberalism (for the free tech). It may be worth it to dedicate a lot of your cities to science specialists for a little while. Especially at higher levels when the AI's science rates become more competitive, getting a free tech can help keep you in the ballgame. On the other side, if you get attacked by a large force, you may want to go pure income for a time to upgrade your troops for the fight.
4) Specialists can give a further early game advantage. If you look at a science specialist, he gives +3 beakers. Now assuming for that your running at 100% science, that's 3 commerce. For a non financial civ, it can take a while before cottages give that kind of commerce, so its actual a boost in your overall output to go scientists. However, your growth rate will ****** as a result, which is why its a good idea to only do this when your near your population limits.
However, lets say you get representation early through the pyramids. Now that's +6 beakers, or 6 commerce. You won't get that kind of output until towns late in the game. In this case, you may find it worth it to go some more specialists early regardless of food, and crank your advantage even more.