well, if you use your starting free ship build point for a geosurvey, a colony ship and a freighter you can start colonize from turn 0 instead that from year 2
to colonize, there is a button from the system screen (f9) but you can just drop anything on a planet and it become a colony.
mars has a low colony cost, so you can bring there 500 infrastructure, population, terraformers, and mines. but that's a bit more work, you should have started with 80 automines so...
queue 2 mass driver on earth.
open the f12 windows, with your cargo group set an order to pick up automated mines on earth and then drop all installations on mars. click the cycle orders check.
now wait til your mass drivers are ready and all the mines are in place. now bring one mass driver (same way you moved the mines) using the 'maximum amount to load' set to 1.
remember to remove the cycle orders or you'll find all the mass drivers on mars!!
now go to mars. you should see the auto mines auto mining, and with the mass drier the target dropdown should contain available destinations. set the driver to fire minerals at earth.
done!
now, for population: build 500 or so infrastructure at earth. same way as above, bring it all to mars.
open the colonization task group, the special order tab. there should be a primary order and secondary order.
set the primary to be 'load colonist at 25m+' and the secondary to be 'unload colonist <25m'
this will bring automatically people from populated planets to unpopulated ones, up to 25 million people.
now, for terraforming: build 5 terraforming installation (I use ship, but let's keep this basic)
bring them to mars, the same way as you brought other stuff.
now on the f2 screen, open the environment tab.
configure it as follow: selected gas: oxygen, add gas to atmosphere, 0.1 and click save atm
congrats, you're terraforming!
now open the f4 screen. select leader type: civilian administrator. pick one with high terraforming or high mining. select mars. click assign on the low right corner.
and now you're a pro!