How you remove carpet depends on how it was installed, but it's a fairly easy task to pull it up. Once it's removed, the choice of a new pad is important for new carpet.
Pulling up carpet is a relatively easy task although when rolled up a carpet can be very heavy, bulky and difficult to move. If there's no need to save the carpet it is easier to cut the carpet into smaller sections with a utility knife and move the sections out one at a time. It's usually easier to cut carpet from the back so when cutting it into small sections, fold a section over revealing the back then slice through the woven backing with a utility or carpet knife.
Pulling up carpet depends on the reason the carpet needs to be pulled up. If the goal is simply to get the old carpet out of the way, protect your hands with heavy gloves and use a sharp utility knife to cut a border around the entire area, about four or five inches away from the walls. Then just lift out the center section, pull up the remaining border of carpet and remove the underlying tack strips along the perimeter.
If, however, you simply want to pull up a small section to check the type or condition of flooring beneath the carpet, use some pliers to grab a section of the carpet in one corner to wiggle a bit of the carpet up off the tackless strip below. Pull up enough to get a firm hold or to hook a prybar underneath and the pull the carpet off the tackless strip. To reveal the floor next pull up the padding which is often stapled to the floor.
If the point of pulling up the carpet is to replace it, pulling up and replacing the pad will also be required. Unfortunately, the "lifetime" warranty that came with the carpet pad referred to the life of the accompanying carpet. And since most carpet companies will have particular padding requirements in order to secure their warranties, it's generally best to replace the padding when replacing the carpet. Undoubtedly there will be many staples holding the pad down and pulling all them up will require crawling on the floor with a screwdriver and needle nose pliers to pull them up. Do not leave staples in the floor if you are replacing the carpet.
Additionally, different carpets require different types of pads. Depending on the pile and fiber content of a carpet, basic padding made from recycled fibers (commonly known as rebond) will usually work fine. The two types shown have slightly different compositions -- the green top sample is lower-density rebond, while the second from the top is a high-density version. The white padding sample at the bottom of the stack is a high-density foam sealed with a vapor barrier, which will resist stains that may seep through the carpet. Most higher-priced carpets will require this type of pad.