Hello Jay,
All you have to do is sign up for the hosting plan of your choice. After that you have two options.
I. You just change the DNS for your domain name and have it where it is registered at the moment.
II. You transfer over the domain name to eukhost as well.
To be honest, the first one is the easier & faster way of having you setup here. I am guessing you are looking for a linux hosting plans. After you sign up with us, if its a shared hosting plan, your account would be setup in about 30 to 40 minutes. You would have to upload your files & off with your
web hosting with us. The DNS propagation has to be allowed between 12 & 48 hours to take effect.
Let us know if you need more help.