You aren’t allowed to use candlelight for detailed activities on Shabbos at night or in a dark room. This includes removing lice from clothing, reading and checking tsitsis. You might come to tilt the lamp and burn the fuel for more light. (ShA1-MB1,2)
This prohibition applies even when you cannot possibly tilt the lamp. E.g. lamp very high up, encased behind glass, fastened to the wall. (ShA1)
Some poskim apply this prohibition to wax candles as well. Even so, those modern lamps that are never tilted even during the week aren’t included in this issur. (MB 4)
If the text that you want to read is somewhat familiar, you may read by lamplight — there is no worry of tilting. E.g. Shabbos zemiros, siddur, Haggada shel Pesach. (ShA 9 – MB 8,9)
Another hetter is if you get someone to watch you so you don’t tilt the lamp. You must verbally inform this person. (ShA 3 – MB 10)
Do not read by the fireplace lest you come to stoke it to brighten the flames. If you get someone to remind you, it's okay. (ShA 5 – MB13)
Another hetter is reading by lamplight on Yom Kippur. The awesome mood will keep you from tilting the lamp. (ShA 8)
The children should not be naked in front of the nairos. It is disgraceful for the mitzva. (Rama 12)