This is what you need:
1) A bright south facing window or a bulb with about 4000K-6500K rating.
2) Some basil seeds, a plant pot and soil from your local store.
Step 1: Germinating
Take some seeds and put them onto the soil. Spacing from seed to seed should be about 2 cm (1 inch). Don't cover them with any soil, as basil seeds need light to germinate.
Cover the pot with a piece of glass or some plastic wrap to keep the soil moist.
Then put the pot to an bright warm place. About 20-25°C should be fine.
After some time the seeds will turn slightly blue. Don't be shocked. That's absolutely normal.
A few days later your seeds hopefully germinated.
Step 2: Growing
Let the soil dry out completely before you water it again. This helps the plant to get a strong root system and it also prevents the plant from pests.
Step 3: Harvesting
The correct way to harvest basil, is to only use the top of the plant. This forces new side shoots to sprout and your plants will get stronger and produce even more leaves.
Eat it fresh, on your pasta or on your pizza. Just put it everywhere you want :)
Have fun growing and enjoying your own basil.