Firstly, make sure you know exactly which partition is which, by their device names (eg /dev/sda1 etc). When you get to the partitioning step of the installer, you have to choose the manual method.
Start with the root partition, look for the "use as" field, and select the filesystem you want to use. If you choose the same filesystem as what's already on the partition, you get the option to format or not format. Every partition aside from /home should be formatted in this case. Then you need to select the mountpoint, there should be dropdown menu with all the UNIX hierarchy directories on it. Select / and move on to the next partition. If you like, you can tweak the mount options also, I like to add "noatime" personally.
For /home, you need to make sure you select the same filesystem as the one which your /home partition is already formatted with. For formatting, you need to make sure you select "No, keep existing data". Then select /home from the mountpoint dropdown. Again, mount options are up to you, but generally noatime is the only one you should consider bothering to enable.
If you have an existing swap partition and don't want to change it, you can just ignore that partition's entry, it will be automatically formatted and used as the default swap partition.
Once you're ready, the next screen will give you summary of the changes, which partitions will be formatted, with which filesystem(s), and which will be used as-is. If there it says it's going to format your /home partition, make sure you go back and do not proceed. It's all pretty straightforward if you know the least bit about device names, mountpoints, and filesystems.
Good luck, though you shouldn't need it.