There are 2 ways:
A lua script that loads the mission (like the mission selector from daboss's mega mod) and the rename method in scripts.img.
Im not sure about the first method but I think it's RunMission. For the second one you have to rename the arcade machine to the mission you want to play.
For example if you want to play "Nice outfit" you have to rename ArcRace1.lur to Test4_05.lur and the other way around (otherwise the game will freeze when you start the arcade machine). There are 2 scripts of each mission, the mission script itself (4_05.lur) and some kind of a mission loader (Test4_05.lur). I mention this because there are some missions where you have to run the loader and other ones where you have to run the mission itself. For example if you run 2_B.lur (dishonorable fight) you get stuck in the ring and in 5_B.lur (showdown at the plant) you can't open the first door, so load the "Test" version. Other example is if that you run Test3_B.lur (fighting johnny vincent) rather than 3_B.lur then nobody spawns and you have to ctrl alt delete the game to exit LOL.