I get questions all the time about removing staples when re-upholstering.
What are the best tools?
Do I have to remove all the staples?
STAPLES - - - the bane of my existence!!! I hate those pesky staples too!! When I first started re-upholstering I thought I needed to get every one of those boogers out - - I have now come to the conclusion that unless they are sticking up - - they are not going to get in the way of my progress!! So no - - -don't worry about pulling them all out - - make sure you have a smooth surface to work with, but if that smooth surface happens to have 50 staples in it that are flush against the frame, I still don't worry about it.
I have found a great tool for removing staples - - at Harbor Freight they have a heavy duty staple remover that you just put under the edge of the staple then rock it back and the staple pops right out.
I love it!! And for $2.99 you can't go wrong!! (BTW - - - pick up a big magnet while you are there, then you can just pick up all your staples with the magnet and not ruin your vacuum or step on them!! It's my little trick!!) Often when i am removing staples, I will use that tool and loosen them all, then go along the entire side using my wire cutter pliers to pull them all out.
When taking off the old fabric, you are going to start by removing the dust cover on the bottom of the chair, then the skirt if your piece has one, followed by the back of your chair, the front of the chair, then the arms and finally the front of the back. Take pictures as you remove each piece, so you can refer back to them as you are putting your piece back together. When you are putting your new fabric on, you will do it in the opposite order that you took it off. So your first piece back on would be the front of the back, seat, arms etc. and finally finishing with the back of the chair and the dust cover.