Since Morphology of Biblical Greek is probably more indepth than you need right now, and so that you don't have to buy any more books, I'll try to give you some of the rules that can help you out. The big thing to understand is that the present stem is NOT the basis for the rest of the stems, rather the verbal root is usually modified in order to form the present stem. So when you look at the principal parts of a verb try to discover what the common verbal root is and then see how it is modified to form the present stem. Here are some of the rules taken almost verbatim from Mounce's Basics of Biblical Greek, I'm not at home and this isn't my computer so I can't download the Spionic font. Here's how I'm representing the Greek (w=omega, v=nu, n=eta, z=zeta, th=theta, x=xi, ch=chi, ph=phi, ps=psi) * represents a verbal root:
1. The present tense is by far the most 'irregular' because the verbal root has often undergone some change in the formation of the present tense stem.
-Single lambda becomes double lambda (*bal>ballw>ebalov)
-Iota is added to form the present tense stem (*ar>ari>air>airw>nra)
(sometimes iota sigma kappa is added, *apothan>apothvnskw with the iota subscripted)
2. Verbs ending in azw and izw have roots ending in a dental. Once you recognize that, the other tense stems are usually regular.
*baptid>baptizw, baptisw, ebaptisa, -, bebaptismai, ebaptisthnv
3. When a verb undergoes ablaut (the stem vowel changes), it is seldom necessary to know what stem vowel will be used in a certain tense. It is most important to use this clue to tell you whether a verbal form is in the present or not. If there has been ablaut, then you know it is not in the present tense, and you can find other clues as to its proper parsing
4. It is common for a verb to insert an eta (kalew>eklnthnv) or a sigma (akouw>nkousthnv) before the tense formative in the aorist passive and sometimes before the ending in the perfect middle/passive (ballw>beblnmai; doxazw>dedoxasmai)
This is especially common in -izw and -azw type verbs.
5. The letter before the tense formative in the perfect middle/passive and aorist passive is often changed, especially if the stem ends in a stop (stops will aspirate to match the theta, agw>nchthnv). It is usually not important to predict what the new consonant will be; just get used to seeing an unusual consonant there and look elsewhere for clues to the verb's parsing.
6. Square of stops plus sigma:
Labials (p, b, ph) + s > ps
Velars (k, g, ch) + s > x
Dentals (t, d, th) + s > s (Dentals drop out before sigma)
When I learn a verb I learn the root with it, I memorize the present (baptizw) and the root as well (baptid). Equipped with only this information I can usually recognize all of the principal parts. Some verbs have multiple roots, i.e. legw and horaw. Keep that in mind and memorize the different roots. Some verbs, very few, undergo so much change that it's just easier to memorize the different parts. Basically, when you see a verbal form, look for distinctives to tell you which tense it is (s = future, theta eta = aorist passive, theta eta + s =future passive) and then try to reconstruct the verbal root from what's remaining. Once you get used to looking at verbs this way it becomes fairly easy. For instance, as soon as I see a verb like baptizw that ends in -izw, I instantly know that the root ends in a dental and it will drop out in every tense that uses a sigma. I don't know which dialect of Greek you're learning but I hope this helps. Also I'm assuming you're not having difficulty with noun morphology, but if you are, I can give you the rules that govern them too.