The best resources I know are a pair of books by French composers, André Gedalge's "Traité de la fugue" and Charles Koechlin's "Étude sur l'écriture de la fugue d'école". This is possibly because scholastic fugue (fugue d'école) is very much part of the French Conservatoire system's curriculum, while it seems to be very uncommon in the English-speaking world, so it helps if you can read French. (If not, Google Translate doesn't cack up French to English translations too badly.)
The Gedalge book is available at IMSLP, specifically here. If you haven't already bookmarked IMSLP, do so: it's the largest repository of Public Domain music literature around. It not only has scores, but books on music and music theory in PDF form. (I'd link directly to the category indexes, but this is my first post here and I haven't got the rep points yet for lots of links.) I can pretty much guarantee you'll find other books on fugue there, in English and in other languages than French. You'll certainly find fugue scores there, and that is even more important.
The idea of fugue is pretty straightforward: it's a procedure rather than a form, really. You introduce each voice with imitative entries of the subject, usually at the tonic level and transposed to the dominant level (subject and answer), and each voice continues fairly freely after exposing its subject entry. The initial exposure of the subject in all the voices is called the exposition. You may need to make tonal adjustments to the answer to keep it from modulating away from the tonic too quickly. (The Gedalge book goes into how that's done in some detail.) The continuation of a voice after the subject may involve a countersubject that is played consistently against a subsequent entry of the subject in a different voice. (That is to say, one voice exposes the subject, then continues with the countersubject as the next voice comes in with the subject.) If you already know your invertible counterpoint, this isn't particularly tough to manage.
Between groups of subject entries (and sometimes between single entries), you have freely-written material (episodes) that may involve sequences and invertible counterpoint, and are usually based on motifs from the subject and/or countersubject and/or free material from the exposition. These episodes usually serve one of two functions: modulatory or cadential (i.e., as a kind of codetta).
Note that the bare minimum fugue involves an exposition, subsequent entries of the subject, and episodes between these. Everything else is optional, whether countersubjects, invertible counterpoint, stretti (overlapping subject entries; the singular is stretto), or multiple different subjects (double or triple fugues, etc.). Sometimes, for stretto fugues (i.e., for fugues that continuously overlap subject entries), even episodes are optional - see Bach's Fugue in C Major from WTC I for a stretto fugue that has very little in the way of episodic material.
Now, from a practical point of view, variation in the sense I think you mean doesn't enter into the writing of fugue too much: variation at the thematic level is rather rare; variation at the motivic level, quite common, but not of the subject itself (except when the variation is used to form a distinct section of the work, each varied subject in effect starting a small fugue within the piece - see J. J. Froberger's canzonas and capriccios, which can be found on IMSLP, as examples).
The biggest problems I usually see are problems of handling the composite rhythm of the voices when played together: either the voices all move in lockstep (which is really just writing in block chords), or they articulate every quaver (or semiquaver, or whatever the unit of background movement is) between them (counterpoint by Singer sewing machine, so to speak). Your voices are freely expanding melodies, so you do want some rhythmic differentiation within them and between them. If one voice is using straight quavers, for instance, arrange that the other voices are using longer and more irregular rhythmic values. This is where your counterpoint studies come into their own: all your appoggiature, suspensions and passing notes will not only allow you write the voices melodically against the implied harmonies, they will allow you to articulate the fugue rhythmically. This is no less important in a fugue than in a sonata. You want your voices' rhythms to come together to put weight on important cadences; you want enough rhythmic incompletion and momentum that the voices don't come to a complete halt at an internal cadence.
Are you finding specific problems when you try to write a fugue? When to bring a voice in with the subject?
Most of the time, when a voice drops out, it does so on a cadential melodic note, usually the tonic or dominant of the current key. When it comes back in, it usually does so with a subject entry, and, of course, the entry is going to come in when the harmony and beat can support its incipit or opening motif. Subject entries usually stand out when they are at the top or bottom of the texture. For alto or tenor entries that need to stand out, it is usually a good idea either to drop out the voices above or below that might obscure the entry, or to hold them fairly static (so that the melodic changes in the internal voice are noticeable).
If you have specific examples of problems, they're usually easier to address than trying to explain by elaborating the big picture.