You can go into the settings on Steam and change where the default install location for your games is. It won't move games you already have installed (you'd have to uninstall and reinstall for that), but it makes it easier to install on a different location.
The C: drive *must* be where the operating system is installed. Without more information, it's hard to say what difference it would make installing a game on D:. If it's a single hard drive that has been partitioned to behave like 2 different drives, you won't see any performance difference at all. If it is two separate hard drives and they are both similar in style, installing on a drive other than C: will give the slightest of performance boosts, as your system can do read/writes for your game while simultaneously doing read/writes for the OS without them getting in each others' way as much. However, if your C: drive is small, it's likely that it is a solid-state drive (basically a fast internal SD card) while the D: drive is a traditional platter-style drive. Platters are much slower to read/write with, so moving to D: might slow down load times in the game. However it will reduce the wear and tear on the SSD, allowing it to last longer.