At the DNS setting for your domain (most providers provide such settings), you have to add an A record and a CNAME record. The A record needs to point to the IP 126.96.36.199 and the CNAME has to forward the www.YOURdomain to the plain domain you purchased.
Lets check out an example in which the new domain is domain.tld.
The A record has to have the domain name entry empty, the IP address entry needs to be 188.8.131.52, as you can see in the picture.
The CNAME record should have as hostname/alias www and for destination domain.tld.
You also have to enable at espivblogs the wpmu domain mapping plugin and from tools -> domains add the domain.tld and the www.domain.tld as domains, without changing the primary domain.
Having done the above, inform us so we can do the necessary changes on our server.