I've been playing for about a month now and I have not figured out how to trap souls and put them into soul gems yet. I keep buying "petty soul gems" that have "petty" soul in them from merchants. I have had and sold plenty of empty soul gems, used the soul gems to charge my enchanted weapons. But how do I trap souls and put them into the gems? Have I not read the right book yet or what here?

Buy a soultrap spell, or get a soultrap-on-strike weapon. Make sure you have empty soulgems in your inventory. Cast soultrap [or use the enchanted weapon] and kill your target before the effects end. You should get a message "You have trapped a soul". You can't soultrap npcs in Oblivion unless you use a black soulgem. The UESP should have more information; its been a while since I've played.

In order to use a Soul Trap spell, you need to have a Mysticism level of 25. You also need to have the right sized gem available. If the creature you kill has a Lesser soul and all you have is an empty Petty Soul Gem, you won't be able to trap it. The reverse is not true however, and you can end up wasting a Grand Soul Gem by trapping a Petty soul.

If you're going to be recharging a lot of items, it would be a good idea to get Azura's Star if you've reached level 2. It holds captured souls and is refillable over and over. It can be very valuable to you. It's a Daedric shrine quest and you can get Azura's shrine marked on your map by:

Reading the book Modern Heretics,
Speaking to Trayvond the Redguard in the Cheydinhal Mages Guild about "Daedric cults",
Speaking to Ulene Hlervu of Castle Cheydinhal about "Cheydinhal" followed by speaking to her about "Daedric shrines",
Speaking to Borba gra-Uzgash at Borba's Goods and Stores about "Daedric shrines" after having spoken to Ulene Hlervu about "Cheydinhal".
credit: UESPWiki

Also, in the Main Quest, Martin needs a Deadric artifact too but DO NOT give him this one. I usually give him the Skull of Corruption since I think it's rather evil.

I already gave martin the deadric artifact so - oh well, I can always play again with a different character. Why? what will happen if I give it to Martin? Anyway Thanks for your help. I have another question if you read this. I'm a level 3 player and I was trying to get some sleep. Well, I woke up a vampire and if I go outside, my health drains out. How can I not get the vampire disease? This happened with my last character I created too.

You became a vampire because you contracted Porphyric Hemophilia, the vampire disease, and failed to cure it within 3 days. When you have just the disease any method of curing a disease will work, but now that you have slept after having it for 3 days you are a full blown vampire. To cure vampirism you must complete the vampire cure quest. You can find a walkthrough of that quest here: http://www.uesp.net/wiki/Oblivion:Vampire_Cure (I think it goes without saying that a walkthrough of the entire quest contains spoilers... And yet here I am saying it ) Once you cure it you can never become a vampire again, so make sure its what you want.

There is also a way to cure it in the Vile Lair official DLC if you have that, or with console codes if your on the PC and don't want to bother with the quest. You can find info on both of those at the same website I linked eairler.

As for giving martin the artifact, what happens is whatever artifact you give him is gone for good. The reason to not give him azuras star is simply that it is likely by far the most useful daedric artifact in the game for any char class. If you enchant items as a mage, or just use enchanted items as a warrior, having an endless supply of soul gems is priceless. So most people give him an artifact that they wont use in their current playthrough instead.

Mysticism Soultrap spell requires a skill of 25 to use. Or you can find a soultrap weapon to use.