How to delete contacts on iOS 6.1.2 iPhone 5?

I just bought an iPhone 5 a week ago and I'm already having problems. It won't let me delete contacts and I'm getting frustrated because before the update it would give me the edit option. It automatically updated and I don't know how to revert it without a master reset, which I don't wanna do because I already loaded all my contacts.

What you do is,
• Go on the contact and edit then go down and there should be a delete button
• or you can just slide from right to left (on the contact) then you'll see the delete sign. But no need to click on the contact. Just go on contacts- then choose whatever contact you want to delete,(don't tap) then on the bar just slide from right to left.
Example
Contacts
My phone number:123456789
Bob sponge. A
Patrick star <- B
<- means slide from right to left. If this won't work, i don't know

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