First of, you will not be able to farm/mine everything on Storis II unfortunately.
But Step by Step:
0 - you need the Portal Epic Skill (5 points) in the EPIC-2 category
1 - Select a Destination Portal.
Your goal being In the Alpha Portal Station you need to buy a Portal Token from a shop stand next to a portal. If none is left try to contact the owner of the Portal Station.
2 - Setting up the Portal on your side.
2.1 You need Portal Conduit Blocks depending on the form/size of the destination Portal.
Most often 2-4 Blocks.
2.1.1 You can craft them with a powered Workbench. You will need 1000power, so diamonds from Serpentsarindi or you can buy them (shameless plug) at my shop in Myra on Finata.
2.2 - Build the your portal exactly in the same form/shape/number of blocks as the destination Portal.
2.3 - Put the portal token in your portal
3 - Activate the Portal.
You will need oort shards extracted from oort stones to activate and fuel the portal.
3.1 You can find oort Stones in Meteors dropping on T3&up Planets. You can buy those too, but doing meteors is fun and good for lvling, just put a few points in vitality and kinetic armor and you’ll be fine on T3 worlds.
4 - Enjoy.
edit: added skill req - thx TheBirne