I have used my old domain for two months and I have do some link building works ,now I find a new domain which I think is better for seo,so how can I use that new domain without any problems?And the backlinks are still there?
You can forward the old domain to your new one and any clicks will pass through, but your new domain will not get any seo benefit from the links.
This is not a permanent redirection, here is META tag used to redirect old page to the new page on new domain. So, if you still have an old site hosted on "free" hosting, and want to move that site to new domain, make and upload (different) page with the same name, add redirection META tag with 10 - 15 seconds, add page moved, bla, bla... in body, with link to newdomain.com/samepage.html, and your new site will be indexed fast.