The answer to this question varies. Depending on the web host that you choose to order service from. The setup time can be in a matter of a few minutes to a few days. Typically web hosts will screen their new customers during business hours but if the web host uses an automated system for making sure there is no credit card fraud then it can be within a few hours.
Shared web hosts plans
If you are ordering a shared web hosting plan, the setup time may be within a few minutes to a few hours. If your web hosting provider is a small business then it may take one business day for your web hosting account to be setup and ready to go. If the web host is a large corporation then it would typically be a a matter of a few minutes minus any credit card fraud checks they may have to do.
Virtual private servers
Depending on the VPS web host your account can be setup and ready to go within a few hours. Some VPS providers may take a few days to get a VPS provisioned and ready for you to use.
Dedicated servers typically take a few hours to a few days. If you are ordering a standard dedicated server configuration then it may take a few hours. If you are ordering a custom configuration then it may take a few business days. If the web host you are ordering a dedicated server from has a lot of servers on hand then it won’t take more then a day to setup.
If you plan to colocate your server with a datacenter. The datacenter would have to verify your billing information is in good standing. They will also have to setup the account before providing instructions on how to send to them your server. After your server is received by the datacenter it may take a few hours to a few business days to get connected to the Internet.