Food52 has a number of good guides to making dishes and sauces without a strict recipe, including this one: How to Make Any Pesto in 5 Steps.
Once you do it once or twice, you will more or less be making it without a recipe.
I’d encourage you to skip basil and pine nuts and go with other greens and nuts, especially greens you may have in your fridge that are about to give up the ghost. I found that the combination of the oil and the greens give the pesto it’s sauce quality, while the nuts and cheese and garlic give it the flavour. So if you don’t like garlic (really?), drop it. Likewise if you have nut allergies. For additional flavour, add some wine vinegar, balsamic vinegar or lemon juice to taste at the end. And of course, add salt to taste.
Why you should make pesto is easy: once you have it, you can add it to food in all kinds of ways to make your food tastier. It is a very versatile sauce.
Once you have pesto, you can add it to roast meats or vegetables. I opened up a boneless pork roast, spread it on the inside, and closed it up. You could do the same with a boneless chicken breast. (Or add some to just cooked fish.) I tossed my roasted vegetables in a bowl with some pesto until they were lightly and evenly coated.
Another idea is to make a pasta sauce with 2 parts pesto to 1 part cream and warm them in a pot while you cook some pasta until it is al dente. Then drain the pasta and toss it with the sauce until the pasta is covered.
If you have some tomatoes, quarter them and lightly toss them with some pesto for an easy salad.
Or take 1 part mayo and 1 part pesto, combine, and use as a sandwich spread.
Lots of ways to use pesto. Enjoy!
(Image via a link to the Food52 post.)