The only way to safely remove vinyl siding is with a specialty implement known as a zip tool. It has a curved, hooked edge that can be slipped up under the edge of the vinyl where it locks into place with the piece below, at which point you can pry the locking mechanism apart and separate the two pieces. You cannot separate vinyl siding without this tool.
One of the most important aspects of removing vinyl siding is to work carefully. This is especially true with wrapped siding that works its way around the edges of a home. If you try and rush the job, you may rip the pieces of siding, and these tears can work their way up through multiple pieces, causing more damage than what was initially done. Work slowly and take your time, moving inch by inch to avoid unnecessary damage.
Regardless of what type of vinyl siding you have on your home, there will be some type of waterproofing material installed behind it. More often than not you will need to replace this waterproofing or at the very least patch it during the repair process. Refer to the siding manufacturer's guidelines for the proper type of waterproofing and how to patch any damaged sections.
Once you have removed the damaged section of vinyl siding, you will have to reinstall a new piece, which means following the siding manufacturer’s installation instructions. These instructions will vary by manufacturer but generally involve nailing a siding section in place while at the same time snapping the upper and lower sections over and under the pieces above and below to lock it in place. Similar to removing the siding, this is a slow, painstaking process to avoid damaging the surrounding pieces.