Get the book 'singer upholstery basics' it is very instructional and full of color photographys of projects just like yours.

i've attempted a similar project - the singer book mentioned above is the best i've found... make sure to set aside enough time to work slowly on it AND it helps to use the previous covering as a pattern (easier to modify than going from scratch)
Good luck!!

Make sure you have the proper equipment, a nail remover & stapler which you can buy at an upholstery store. Examine the piece & start pulling out staples (which you will begin to find) carefully. Once you have the fabric off you can remove padding, cushions, etc but it may be a good idea to document each level/step with a cameral so you have a reference to go back to when reconstructing. Do not cut the fabric, use the old fabric as a template to cut your new upholstery. Then it's just a matter of following the steps you used to take it apart, but going backwards of course. You may also want to get a fabric stretcher (a little tool that has metal teeth that grip the fabric so you can pull it tight and then staple it down). I don't know if your ottoman requires any sewing but if you're not adding the skirt, it shouldn't. Ottoman's are fairly simple to reupholster. You'll learn as you go along, just be patient! :) Good luck!

daughter of an upholsterer here! another handy item is a tack strip. it's a heavy cardboard strip with tacks embedded in it. you put it on the inside of the fabric and fold it over so the cardboard strip is covered and the tacks press into the frame of the furniture. it's great for keeping a straight line and avoiding puckering. in the past, i've just gone into an upholstery shop and asked for a couple strips. i offer to pay but usually the upholsterer just snickers and gives them to me. :) it's like offering to pay for a packet of ketchsup at a restaurant; they probably cost him $1 each.

i'm in no way a professional but when we reupholstered a chaise lounge i actually left the covering on bc it held the padding onto the frame (it was very old). it may be a good idea if you are too afraid to start taking it apart - this way the main structure is kept in tact and you can just work from to build it up as you want.
that said, getting rid of the skirt may be tricky.
but as advised above, go slowly, keep your patience and leave a lot of time

If you do document your project why not enter in the January Jumpstart--sounds like a very worthy project!

I've done some upholstering and it's not too difficult. However, first I'd try to removing the skirt and then making a slipcover to put over the existing cover. You could use velcro to attach flaps of fabric neatly underneath, so the legs are revealed. Or you could staple the fabric in place.