Redirect links can be done using several methods.
If you want to redirect your domain or subdomain, you can use this method. The steps and UI really depends on the registrar, but usually it is similar to the other. I use namecheap, and here to do it.
You can also do it by editing the CNAME records.
Shortener like http://bit.ly can be used for link redirection. You need to subscribe to their paid plans though. I use another shortener that I get from AppSumo at a bargain price. You can check to their site at AppSumo to know if there is similar deal. You can also get $10 off.
Using WordPress Plugin
If you are using WordPress, you can use several plugins available online. One of them is Affiliate Links — WordPress Plugin for Link Shortening and Masking from CodeCanyon (Envato group)
If you are a software engineer, you may write your code yourself. There are many tutorial online that you can try.