How to delete photos from my iPhone?

Okay okay. The title might seem vague but here's the body of the problem. I've just got rid of my blackberry and got an iPhone 5. I'm really enjoying it and everything, there's just a couple of slight problems. I transferred all of my blackberry images onto my computer and later onto my iPhone. So on my iPhone I have a couple of album titles like 'old blackberry images' and so on. My first problem is that when I go onto the images in these albums, I can't actually delete any of them without scrawling through hundreds on the computer and doing it manually. Is there anyway I can set my iPhone to allow me to just delete them straight off the device? Secondly, is there anyway I can just have 2 folders, one being 'photo library' and the other 'camera roll' as opposed to having several with names such as 'old blackberry images' or 'summer holiday 2012'? I do have the 2 aforementioned albums, it's just that the only images in the photo library are a collection of all my albums, seems a bit pointless and needlessly cluttered. Apologies for the ridiculously long winded post, it's just that I could really do with sorting these! (The first problem is one that I'm most keen to fix!). Many thanks in advance!

Added (1). Sorry guys, didn't make myself entirely clear! There's NO way whatsoever for me to delete the images off the iPhone. I know exactly how I would do it as I've had the iPod touch for the last year but there simply isn't any form of delete button anywhere. Perhaps i should just phone Apple or visit one of their stores! Cheers!

What kind of photos are we talking about here…

Pop down to a Apple store they will show you, how, when, why, what etc about your iphone

If you want to delete certain photos from your phone if you scroll through them you should see a bin symbol appear in the bottom right hand corner. If you select that you should be able to get rid of the pictures you don't want. It might be different cos you have uploaded from a computer but i don't see why.

Ok, I'm guessing you have loads of photos!
Instructions:
1) scroll down to that icon on the bottom left of your screen!

2) press on the icon!

3) there should be faint buttons saying delete/ add to/ send and others! ( on the right top there should be a cancel button in blue)

4) tap on the photos you wanna delete then the red delete button on the bottom right should just be more vibrant!

5) press on the red delete button and the photos should be deleted instantly!

Hope this helped!

Just tap the little trash can in the bottom right, if it doesn't show tap the photo then it appears.