This will depend on what the file name of your current home page is.
If you are lucky, the file for your current home page will be 'index.html' or 'index.htm'. If it's anything except 'index.php' you should have no problems. If this is the case you can upload WordPress and run that basically alongside of the site you have now. WordPress will not affect your current pages, and will only be used when a user requests a URL that's not an existing file. When it's ready you can remove the index.html file and your homepage will automatically flick over to WordPress. The downside to this is that it has the potential to get very messy digging around with two different systems in one spot.
If you are already using a home page file called 'index.php' them the best idea is to install in a sub-directory or somewhere else, do your work on the site and transfer it. There's a lot of resources around that can help you out with that one. The main thing that you'll need when moving the site is that you'll need to use a tool to update your database to change the hard-coded image/media/link URL's from the old site to the new site.