Oh, quite simple.
Step 1: Get a lot of money.
Step 2: Get a group of engineers that seriously know what they are doing.
Step 3: Get permission from your government to launch what is essentially a bomb into space...
Step 4: Build the vehicle and launch facility. You will likely need involved technical know-how (the engineers can help) and more money (inconel and alu-lithium alloy doesn't come cheap...)
Step 5: Train yourself and your equally crazy friend. Not sure, but I wouldn't be surprised if Star City would allow you to complete basic astronaut training (at a price, of course).
Step 6: Light the contraption, and pray, because there isn't much else you can do to prevent the 99% chance that it will blow up with the force of a small atom bomb...
Seriously, no one person would be able to do this (IMO the main reason comes down to money; even professional ventures have failed).
There have been people (such as John Browning, the inventor of countless firearms, who managed to fabricate prototypes and such from his home in the middle of nowhere in Utah, in a time when fast transport was nonexistant) who were clearly geniuses and extremely dedicated to their work, however.
Perhaps if a "kit spaceraft" (at least one where a set of foolproof plans were available) existed, it would be possible to do so. But the undertaking would still be immensely expensive.
A more realistic goal would be a simple, one-off, one person suborbital flight. But you'd still need money and expert help (or at least brains) to pull it off.