Galacticraft is a a mod in Attack of the B-Team that allows you to explore the solar system in your own spaceship. It adds ores such as silicon and aluminum to the game. These can be used to craft the parts you need to build a rocket and blast off to the moon and mars.
Use Not Enough Items to find the recipe for a tier 1 rocket. You will need a NASA Workbench in order to craft a rocket. Once your rocket has been crafted you will need a launch pad, rocket fuel loader and rocket fuel along with energy to fuel your rocket and blast off into space.
As there is no oxygen on the moon you need to craft oxygen gear and tanks to allow you to breath. The tanks can be filled up with an oxygen collector connected up to an oxygen compressor.
Once you have landed on the moon plant a tree and place an oxygen collector hooked up to an oxygen collector like previously. Also hook up an oxygen bubble distributor to create an oxygen bubble, within which you can breath without requiring oxygen gear.
You can jump high on the moon due to a lack of gravity. You will want to mine any meteors you find as they will help you to get to mars.