Take a look at the vim-autocomplpop plug-in, which triggers the completion menu automatically as you type.
For using "Tab" instead of Ctrl+N in the completion menu, you can use a simple mapping such as:
inoremap <expr> <Tab> pumvisible() ? "\<C-n>" : "\<Tab>"
As an alternative, you might want to consider the SuperTab plug-in. It doesn't really do "as-you-type" completion and requires you to use the "Tab" key to initiate completion, but it's quite powerful and it has nice features you might like. (Note that I wouldn't expect SuperTab to work well with autocomplpop, so you might be able to pick one or the other, unlikely to be able to pick both.)