I am a complete camera novice and have a Nikon D5000 camera, and have been given a box of new (compatible) close-up lenses for my birthday.
We can't know for sure from your description, but "a box of closeup lenses" sounds like it might be something like a set of close-up filter lenses like these Hoya lenses. If that's what you've got, then you're in luck -- these are intended to attach to the front of an existing lens. The filters have male threads that should mate with the female threads on the front of your camera lens. If the filters are too big or small to fit your lens, then you can either return them and get the right size (they come in a variety of diameters), or get an appropriate step ring to adapt the filter to your lens. Even high quality step rings are pretty inexpensive.
Another possibility is that you've got a set of extension tubes. These are spacers that fit between your camera body and lens: you take the lens off, attach the extension tube to the lens, and then attach the extension tube to the body. There's no getting around removing the lens if this is what you've got.
Finally, you might have one or more actual camera lenses of the macro variety. A macro lens is a regular camera lens that's able to focus very close and which can therefore magnify small objects. Someone would've been very generous to give you several of those, as each one generally costs a few hundred dollars (or more). So I'm guessing this isn't what you're dealing with, but for completeness let's just say that these won't fit on the front of your existing lens -- you'll need to swap lenses to use them.