I am quite green fingered, but Basil has always been a bug bear of mine. Finally think I may have cracked it. You must prune regularly, wash and dry the cuttings, stuff into a jam jar and cover with a good EVOO (extra virgin olive oil) a pinch of salt and store in a cool dark space. You can then sieve off the oil and bottle it. Some recommend bruising or cutting the basil, but I've found it browns badly and is unusable for pasta later.
Keep your plant moist, but never ever water from the top, pop it in a dish of luke warm water for a couple of hours, also mist regularly. I turn my plant upside down and finely mist. Watch out for any bugs, if you do get any infestation, drape the whole plant in a plastic bag for a couple of days, if this doesn't work, bin it and start anew.
If your plant develops flowers, chop them off (you can eat them in salads), but the plant will lose it's gorgeous smell and flavour once flowers have appeared. You can pop the flowers in an envelope and re-grow, Basil is an annual.
I want to encourage youngsters (male or female) to get into the kitchen and enjoy cooking. TASTE it!