What lens to get for my Nikon D5100?

I want to get some lens's for my Nikon D5100 but I don't really understand how they work!
Okay so I want a zoom lens, portrait one, and a lens that's good for landscapes and animals!

I think you should first read some

anyway

a zoom lens is simply a lens that can change focal lengths
a good portrait focal length would be 50mm for your camera
for landscapes, look at the Nikon 10-24mm or Tokina 11-16mm
for animals, you need a long lens. Look at the 55-300mm or 70-300mm VR lenses

I recommended you to read the article in below source before decide to buy the suitable lenses for your camera.

Lens start at $100 and can go up to 5 figures you sure should have told us your budget.

Prices may not be 100% accurate but it will give you an idea.

Portrait, Nikon fix lens:
50mm f/1, 8D $120 (AF won't work, your camera lack the technology to make it work)
50mm f/1, 8G $220
50mm f/1, 4G $440
60mm f/2, 8D Macro $450 (AF won't work, your camera lack the technology to make it work)
85mm f/1, 8D $465 (AF won't work, your camera lack the technology to make it work)
85mm f/1, 4D $1200 (AF won't work, your camera lack the technology to make it work)
85mm f/1, 4G $1700
105mm f/2D $1050 (AF won't work, your camera lack the technology to make it work)
105mm f2, 8vr macro $950
135mm f/2D $1400 (AF won't work, your camera lack the technology to make it work)

Portrait zoom lens:
Nikon 24-70mm f/2, 8G $1700
Sigma 70-200mm f/2.8 EX DG APO OS HSM $1400
Nikon 70-200mm f2, 8vr $2100
Nikon 80-200mm f/2, 8D $1100 (AF won't work, your camera lack the technology to make it work)

Landscape, wide angle can give you amazing perspective.
tokina 11-16mm f/2, 8 $660
Sigma 8-16mm f/4, 5-5, 6 $700
Sigma 10-20mm f/4-5, 6 $480
Sigma 10-20mm f/3, 5 $650

Portrait zoom lens less expensive:
70-300mm f/4, 5-5, 6vr $500 between 70-200 it's sharp, pass 200 it become softer and I find the Bokeh (creative blur due to small depth of field) a bit harsh with that lens but that just me, and it's a sliding aperture which mean at 300mm the biggest aperture will be f/5, 6.

Sigma 70-200mm f/2.8 II EX DG APO Macro HSM AF $800
Tamron 70-200mm f/2.8 Di LD (IF) Macro AF $730

Note: the 70-200mm & 70-300mm can be use for animal but if you're planning on doing wild life, I would recommend you a greater range because those are most of the time not enough, usually for wild life they use Nikon 100-400mm, Sigma 150-550mm or fix lens like 500mm etc.

Well you can use a lens for anything. Just because it's a telephoto, you can still use it for portraits.

55-200mm, 55-300mm, 35mm f/1.8 are a few great ones.

Here's a Lens Buying Guide - http://www.the-dslr-photographer.com/2009/11/buying-a-lens/