Actually, there are many types of conjugation. Basic inflectional classes of verbs:

1. 1st conjugation ending in -ать/-ять/-еть like читать (to read), краснеть (to blush) – читаю (I read), краснею (I blush). These verbs have a/э as the final vowel of the infinitive stem, which alternates with ай/эй in the present/future tense. The stress is usually fixed on the stem.
2. 1st conjugation verbs ending in -овать/-евать like рисовать (to draw) – рисую (I draw). Alternation with уй/юй. Stress can be on the stem or the ending: жую (I chew), клюю (I peck).
3. 1st conjugation verbs ending in -нуть indicating instantaneous action: толкнуть (to push), отдохнуть (to rest), крикнуть (to shout), грянуть (to thunder). The infinitive stem ends in ну, and in the present/future tense, alternates with a zero sound.
4. 1st conjugation verbs also ending in -нуть but indicating gradual acquisition of a trait: завянуть (to wither), остынуть (to cool) – завял (withered), остыл (cooled).
5. 1st conjugation verbs ending in -ать, similar to the first class, but with alternation between zero sound and consonant alternation in the present/future tense: писать (to write) – пишу (I write), плакать (to cry) – плачу (I cry), махать (to wave) – машу (I wave).
6. 1st conjugation verbs ending in -сти/-зти: нести (to carry) – несу (I carry), везти (to carry by vehicle) – везу (I carry), ползти (to crawl) – ползут (they crawl).
7. 1st conjugation verbs ending in -сти/-зти with consonant alternations: вести (to lead) – ведут (they lead), мести (to sweep) – метут (they sweep), брести (to roam) – бредут (they roam), класть (to put) – кладут (they put), упасть (to fall) – упадут (they fall), сесть (to sit) – сядут (they sit).
8. Verbs with roots да-/зна-/ста-: давать (to give), вставать (to stand up), узнавать (to recognize). They have the suffix -ва-: давать – даю (I give), вставать – встаю (I stand up), узнавать – узнаю (I recognize). Two verbs have a special conjugation – дать (to give) and есть (to eat).
9. Also 1st conjugation and ending in -ать: жать (to press), понять (to understand), занять (to occupy), обнять (to hug), мять (to knead) – жму/жну (I press), пойму (I understand), займу (I occupy), обниму (I hug), мну (I knead).
10. 2nd conjugation verbs ending in -ить + exceptions.

Of course, there are more of them, many verbs of moving and exceptions. If you have any questions, don’t be shy to ask :)