I have a local sharepoint website running.I want to make it some thing like abcdefg.com.How can I achieve this in sharepoint 2010.
You will need to enable anonymous access on your WebSite, follow this link for detailed steps.
Here's another article on how to create a web application in SharePoint with your own domain name
Also get the hosting company to setup the DNS records first. They should all point to the IP address of the SharePoint server. Then create the site collections specifying the names you want to use in the New-SPSite command. Once the HTTP request reaches the SharePoint server it will handle routing the request to the right Host named Site Collection.