The Hard Way
1) Mine
Spend lots of time mining and worrying about inventory space.
2) Transport
Spend 5-10 minutes moving your stuff to town, unable to pick anything else up on the way, and hoping you don't die.
3) Wait
Go around to various shops trying to find a place to sell your stuff, or advertise your shop and wait for someone to buy it from you.
4) Go Back
Go back out to your base again. (Another 5-10 minutes if you walk.)
The Easy Way
1) Mine
Mine resources however works best for you.
2) Bury
Place mined resources in a well-hidden chest.
3) Submit
Submit a report to get paid for your mining. Payment is sent automatically once your chest is verified (within 2 days). You can now immediately continue mining and get more rupees.