I figured this out, in case anyone else gets stuck.
Here's how to do it:
Step 1: Port over your current database. With Umbraco, there's an easy way of doing this. Simply install the Export SQL Server Compact package, an addon to your Umbraco CMS. Once installed, follow the directions and generate your SQL file.
Step 2: Import the generated script to SQL Management Studio and run it in a new database. In order to do this: create a new database and give a new user permission settings to access that database (don't use your server login - you can, but it's better to create a user so you can access remotely). After that, go ahead and copy and paste your entire file (yes, that entire file) into a new query (right click the database -> run query), paste the script, and run it.
Step 3: Change the connection string. This is in your web.config. Within the XML tags of , configure something akin to this (remove the {}):
<add name="umbracoDbDSN"
connectionString="Data Source={the ip of your database};Initial Catalog={theDatabaseName};User Id={theUserId};Password={yourPassword}"
providerName="System.Data.SqlClient" />
The nice thing about this connection string is that you can edit locally, as well as on site, with the same connection string. This allows you to test code changes on your localhost, without changing the code on the website. The only thing that is linked automatically is CMS Content.
Make sure not to delete your old Umbraco connection string, in case you want to revert back to it. Simply comment that out.
Step 4: Encrypt the web.config. Clearly it's not wise to keep your database password in plaintext on your website. This MSDN on encrypting your web.config is invaluable.
There are a few things you will lose with this:
Portability of your database. Sometimes you'll want to only have a file be a database instead of a whole server. We only recommend doing this step when your site is essentially done, as configuring a SQL Server and keeping it secure is an extra challenge you shouldn't worry about.
Occasionally, images don't transport. You might have to reinput all of your images manually.
Possible security. Every time you publish your website, you may have to reencrypt the web.config manually. This can be exceedingly dangerous - so make sure your website always has the web.config encrypted, even on new publishes.