Any time you make a DNS (domain name server) change it takes around 24-48 hours to complete. During this proprogation time routers all over the world are updating their cache. This causes your site to be up and down randomly during the first 48 hours for different people at different times. Think of dns like a zip code. If you don't put a zip code on your mail the post office doesn't know where to send it. Domains are the same way if they don't have the DNS the internet doesn't know what server to send your request to.
Making The Changes
Every registrar has a different procedure for changing your domains DNS, however they are all done basically the same way. The welcome email you received from us provides you with the name servers you need to change your domain to. You will then take those name servers to wherever you bought your domain, and fill them in for your domain name.
Your name servers should look something like...
(do not use the above unless told so in your welcome email)