To complete a space mission, you need to build spacecrafts and send them out to space. Each time you launch a spacecraft, there is a chance that your mission will fail. This means that you might need several tries to successfully launch one. You can see what your chances of completing the mission are by clicking on it in the Space Research Bureau window. It will bring you to the corresponding spaceship which will tell you your odds. Alternatively, you can click on any spaceship model directly to see your odds of succeeding. Example:
Each spacecraft has a number of missions associated with it. Each mission can be completed only once. You can only complete 1 mission per launch. Each launch will bring you income, regardless of whether or not you were actually able to complete the mission. This means that even if you have already completed all the missions for a particular space craft, it still makes sense to keep sending it out to space to earn more coins and experience.
Have fun playing the game!