To start going to planets, first you need to find them!

Step 1: Make an Observatory
Step 2: Put cameras and lenses into it
Step 3: Research the "Find Planets" technology
Step 4: There should be a message saying something like "You found Planet ...!"

Now you can go there!

Step 5: Acquire a rocket
Step 6: Research "Space Survival" Tech
Step 7: Make a "Space Capsule" and put it in the rocket cargo slot
Step 8: When the rocket is finished launching there should be a menu
Step 9: Click on where you want to go, then click "GO!"
(The home planet is called "nauvis", so not there)
Step 10: You should now be on a different planet!

If you want to go back:

Step 1: DO NOT destroy the "Landed Rocket" or you will not be able to get back!
Step 2: Put 100 Rocket Fuel in the "Landed Rocket"
Step 3: There should be the same menu as when the rocket was launched
Step 4: Click "nauvis" then "GO!" to go back home