If you are not going to use fresh herbs immediately after buying them, you should put them in the fridge. Simply wrap them in a moist paper towel and put them in a plastic bag (like a Ziploc). They should keep for about a week.
If you want to preserve them for longer, place the herbs in a glass with 2 to 3 cm of water. Then cover the glass with a plastic bag, securing it with a rubber band. This method will preserve them for 2 to 3 weeks. Don’t wash the herbs until you are about to use them, and only wash them if they are covered with sand and grit. Be sure to pat them dry before using.
Don’t be shy to use fresh herbs in all sorts of recipes, even in salads, instead of just throwing them out because you don’t know what to do with them.
If you use some of an herb in a recipe and there is some left over, chop it up and mix it with some butter. You can then use the perfumed butter to intensify the taste of a steak or grilled fish dish.