Hi Kai Johnson,

I can think of following ways to do deployment in salesforce on top of my mind:-
 
1. Change Set (if you want to keep track of what has been deployed & when)
2. Using Eclipse
3. ANT
 
Apart from above three, there are multiple tools available in market too. But above three are used mostly.

Below is basic advantage & disadvantages of all three:-
 
Change Set :-
1. You can do deployment between orgs you have connected using 'Deployment Connection'.
2. You can keep track of who did deployment of what and when.
3. Very easy for admins.
4. Can't do deployment on adhoc from an org which is not connected through 'Deployment Connection'.
 
Eclipse :-
1. You can do deployment across any salesforce org, you don't need any 'Deployment Connection'.
2. Used by developer, not for admin.
3. You can't track history of deployment.
4. Uses metadata to do deployment.
 
Ant :-
1. As with Eclipse, you can do deployment across any salesforce org, you don't need any 'Deployment Connection'.
2. You can automate deployment to run on specific time.
3. You can automate deployment using automation tool like Jenkin.
4. You don't need any specific UI to do deployment.
5. If you have any repository like GIT from where you do deployment, Ant is best used.
6. You can't track history of deployment.
 
Apart from above point, there are other differences too. Which you can find on http://sfdcbeginner.com/salesforce-deployment-methods.html

Hope this will help you!