To refrain from something is to abstain from an impulse to say or do that thing. The idea of (self-) restraint is reflected in the word’s origins: refrain comes from the Latin verb refrēnāre meaning “to bridle,” or to control or hold back a horse. To forgo something is to give it up or to do without it; a patient might forgo medical treatment or an executive might forgo a bonus. Beware that forgo is sometimes spelled forego, but forego has a meaning all its own: “to go before” or “to precede.” To avoid ambiguity (and to please the editors in your life), forgo the e when spelling this subdued synonym.
To indulge in something, such as a decadent dessert, is to yield to a desire for that thing, or to allow oneself to follow one’s will. This verb is commonly used of things one typically limits or avoids, and so it is bound up with the idea of giving oneself permission to do something or giving in to something that is usually off-limits. To luxuriate in something is to revel in it, or to enjoy oneself without limitation or restraint. Luxuriate implies a more delighted and celebratory kind of partaking. This sumptuous synonym may call to mind extravagance (what we associate with the word luxury), but one can luxuriate in pleasures big or small.
The verb manage is used several different ways. One can manage stress, manage to get by, or manage a business. The last example, in which manage means broadly "to be in charge of," is the closest to preside. To preside is to exercise management or control, the way a lawyer might over an estate or a president over a country during a specific event or time period. The verb's similarity to the word president is no coincidence: the two terms come from the same Latin verb (praesidēre "to preside over," literally, "to sit in front of"). Preside is also used to talk about occupying a place of authority, as in an assembly or meeting: when you preside over a meeting, you are acting as the person in charge.