Next time you're at a Vietnamese restaurant looking down at a lovely bowl of pho soup with a big plate of sprouts and thai basil on the side, you may want to consider gardening. Specifically, that Thai basil... wonderful stuff, very tasty in a wide variety of dishes... and they've just given you a large, fresh sample to plant in your garden. Carefully pluck/snip off all the large and medium leaves from the stems, leaving only the smallest sprouts, break off the basil "branches" from the stem, so that you have a half dozen or so branches, each about 3-5" long. Wrap a paper napkin around the base of these branches, and dip the end of your napkin in your water glass to keep the cuttings moist, and maybe wrap another dry napkin around the damp one, and be sure to take it home with you. You'll get a few odd stares, but it's for a good purpose.
Once you're home, fill a pot / cups / etc. with wet potting soil or other rich, loose, moist soil. With sharp garden snippers or scissors, snip the cuttings at a 45-degree / diagonal angle, and place them into the soil. Within a few weeks, with a bit of care and luck, you should have several Thai basil plants, each of them developping roots... some may die, but generally they're quite hardy, and should produce you a ton of Thai basil. If you really want to increase your chances, dip the stems in rooting compound before putting them in the soil.
Congratulations, enjoy the complementary plants with your meal, and welcome to the exciting world of propagation by cuttings