Cloning Textmate's functionality with Vim
Solution 1:
snipMate.vim
For Textmate style snippet expansion in Vim.
http://www.vim.org/scripts/script.php?script_id=2540
Solution 2:
Command-T
The Command-T plugin is un-do-without-able. It replicates TextMate's Go To File... functionality very nicely, plus of course you can set your own keymapping, and have files open in split windows, tabs, etc.
Solution 3:
NerdTree
For file exploration in Vim.
http://www.vim.org/scripts/script.php?script_id=1658
Solution 4:
If vim is not a requirement (in the title you said Vim but in the text you said how to clone textmate in ubuntu) you should take a shot on emacs.
In emacs you can have a closer textmate experience, with a snap-open (ido-mode) snippets with yasnippet (compatible with textmate snippets) and an editing style a little closer to what you get on textmate.