I dont quite get how to enchant weapons, I am either doing something wrong with the stones or something, can someone give me a hand?

The better the soul in the soul gem = the better the enchantment.

A Grand/Greater Soul is the best.

http://www.uesp.net/wiki/Skyrim:Enchanting

Basically, the strength of the enchantment depends on your skill and the type of soul gem you use (and the size of the soul in the gem).
Besides the black soulgems (which are rare) grand soulgems filled with a grand soul will give you the maximum enchantment for your skill.
Filled grand soulgems can be bought from all the court wizards and some of the other merchants.

Your levels of Gem stones go from Petty, Lesser, Common, Greater, Grand. The WORST is petty use this on rings or necklaces to add more to the value and sell them for more,
Grand soul gems are the BEST to get these you need to kill a mammoth or if you have a Black soul gem these will catch peoples souls that are always GRAND good to take from bandits or some other group of people who can freely be killed.

The weaker your Animal or Undead target the weaker the soul the stronger the target the stronger the soul

You can also use soul gems to recharge enchanted weapons in the weapons menu go to your enchanted weapon and will give you an option to recharge same thing applies here lower the gem the less charge the better the more charge. This also levels up enchanting skill.