Did you put the snipMate directory that you get after unzipping directly inside ~/.vim? Like that: ~/.vim/snipMate?
It's its content that you have to put into ~/.vim:
.vim
├── after
│ └── plugin
│ └── snipMate.vim
├── autoload
│ └── snipMate.vim
├── doc
│ └── snipMate.txt
├── ftplugin
│ └── html_snip_helper.vim
├── plugin
│ └── snipMate.vim
├── snippets
│ ├── autoit.snippets
│ ├── cpp.snippets
│ ├── c.snippets
│ ├── html.snippets
│ ├── javascript.snippets
│ ├── java.snippets
│ ├── mako.snippets
│ ├── objc.snippets
│ ├── perl.snippets
│ ├── php.snippets
│ ├── python.snippets
│ ├── ruby.snippets
│ ├── sh.snippets
│ ├── _.snippets
│ ├── snippet.snippets
│ ├── tcl.snippets
│ ├── tex.snippets
│ ├── vim.snippets
│ └── zsh.snippets
└── syntax
└── snippet.vim
After that, put this line in your ~/.vimrc:
filetype plugin on
and run this command in Vim to make the snipMate doc available:
:helptags ~/.vim/doc
If you do all that, you should be able to read the snipMate doc, which you should do before anything else:
:help snipmate
Good luck.