What are full-time protestant proselyting missions like? I'm a Mormon, and everyone knows Mormons are famous for missionary work, as pretty much every faithful young man will serve a 2 year full-time mission right out of high school, and many women will choose to serve one (or more) 1.5 year missions.

I'm very familiar with the LDS missionary program, but I'm not too familiar with many protestant programs. LDS Missions are pretty simple I think: You go through the application process with your bishop, if he thinks you're worthy then your application gets sent to church headquarters, a few weeks or months later you get a mission call to go serve somewhere in the world for 2 years (the church chooses where you go), you're set apart as a missionary–at which point you start living very strict mission rules 24/7–just before you report to the Missionary training centre for 3-12 weeks prior to being sent out into the field. 

As a missionary you commit yourself 100% for 2 full years teaching people about the restored gospel of Jesus Christ, no days off, no vacation, no TV or cinema or entertainment of the like, and no phone calls home except for on Christmas and Mothers Day on top of a plethora of other very strict rules (no flirting/dating, iceskating, horseback riding, etc., etc.).

That's a typical LDS proselyting mission. There are many other types of missions that you can choose to go on, but for this question I'm only interested in proselyting missions. 

How do some Protestant missions compare?
I come from a family of Protestant missionaries.

From a Protestant standpoint, the definition of a missionary is very apostle Paul-like. You simply have to go teach the gospel where it is not taught. There doesn't have to be a huge process to it.  

The only time tight restrictions and approval processes come into play is when someone wanting to do mission work asks for monetary or other support. In such cases each overseeing organization has vetting processes to make sure a would-be missionary is sincere and reliable. 

Common Examples,

A person decides to be a missionary in China. He or she goes to China, supports himself or herself by trade during the day, spends weekends and evenings teaching the gospel. 

A person decides to be a missionary in Somalia. He or she goes to individual churches or support organizations and asks for monetary support, and will likely have to show evidence of due diligence to be considered. Each church or organization may choose to support or not support on their own.

A mission oriented organization seeks people to go to certain areas. People who express interest are vetted and sometimes put on a probationary or intern status. Sometimes these people must still raise their own funds( which is easier to do with a stamp of approval from a missions organization) or the organization may raise funds for them.

In almost all cases the global restrictions are no where near what they are for Mormons, though many protestant missionaries will self impose certain things like dress codes in order to not offend a particular culture.