I've done this. Three factors that will eliminate nearly every opportunity for you to do it as well:
1. Two full sizes too big, minimum.
2. Peaked lapels. How many suits, really, are there with peaked lapels that aren't dinner jackets or already double-breasted?
3. You have to be or have a real tailor bring in the shoulders first.
So, if you have a suit that fits these criteria then you can do this, but there is no going back. Step 1 have the shoulders split and brought in. That's what my tailor calls it, he pins both right smack in the middle, right through the padding, it looks horrific. I don't much know nor will ever know what he does, he barely speaks English. But the jacket shoulders are perfect and there is no seam that I can find.
Step 2, get a full button set for a double breasted suit coat, seven big and six or eight little for the sleeves. Cut off all the old buttons, fit the jacket and chalk it up. Make a button-hole on the right side where the top button (assuming your project started as a two button coat) was. Install the left inside button, mark and install the rest of the buttons. Note the top two buttons, neither are functional, are traditionally installed a bit wider than the four other front buttons to accentuate the male V shape.
Step 3, close up the vent or vents in the back. A double breasted suit is the most formal if suits, right behind the Tux and tie and tails, so it should have no vents. Two vents are for horseback riding, one is for daily use suits so you can get to your pants pockets, no vents is formal, ostensibly you would never need to access your pants pockets when in a formal double-breasted business suit.
Have at it my friends, I assure you this process when done well will not make your final product look queer, however, it is NOT for the niggardly, as it can be quite pricey.
Did I cover all the bases?