There are couple of ways to deploy components from one org to another org. As @Salesforcemarty highlighted the procedure using Change Set. It is one of the simplest method to move components from one org to another.
Another way is to use a tool called as ANT. ANT can be used to deploy components from one org to another. You need to configure ANT in your machine. Refer this link for configuration of ANT. It is open-source software. Once you've configured ANT, follow below steps:
- First you need to prepare package.xml which contains details about your components which needs to be deployed. In your case it would be something like this:
<?xml version="1.0" encoding="UTF-8"?>
Prepare build.properties which contains credentials of source and destination orgs and build.xml contains commands which are configured for ANT. A Sample code for build.properties and build.xml can be found here github/mrohit/ant
Once all of these things are ready, simply use those commands to retrieve components, validate them and finally deploy.
You might think it is lengthy process but here are some plus points using ANT over Change Set