it depends on the herb.
you can easily chop and freeze cilantro, dill, parsley.
for the woody types of herbs, wrap in moist paper towel in a ziplock baggy, put in fridge.
check every day paper towel is still moist.
you can do this with mint too.
some herbs you can put in a glass jar with water, like parsley, mint, chervil.
you can dry mint well, thyme too. rosemary doesn't dry well neither does basil.
just some 2 cents since you did not say which herbs.
I would suggest buying some pots of herbs and keep them in there, water regularly, is the cheapest way to keep fresh herbs and a nice selection.
most will do in half shade, depending on the herb ......think if the country where it originates and you will know which ones need sun etc.