a) Dry up
Thyme / Peppermint: Should be dried up (if not already) and hang up as a bunch somewhere it gets no humidity (definitely not around cooking area) or grinded by hand and put in a jar with a tight top which isolates air well.
Sage: Dried and bunched as above. Grinding not recommended.
Drying procedure: Wash the fresh herb (separate the branches if in bunch) and put on a paper towel to absorb all the water first. Then put the herb on a large paper with all the branches separated and let to dry up well (It may take some days!) The paper should not be placed anywhere humid.
Testing: If herb gets crashed in between your fingers easily then it dried up well – you can either make a bunch and hang up or grind/crash by hands and put in a jar with tight top.
b) Grow them as "Paul L" recommended
Most of the herbs/plants die just because they are not in proper pot (mostly very small) with proper soil mixture.
Buy a pot of rosemary/laurel bay/parsley/mint, etc. And then change the pot with a bigger size one (big enough to let the herb to grow up) and change the soil as indicated below.
Soil mixture: 2 units of garden soil (from garden/park, etc.) + 1 unit of Turf (from shop) + ½ unit of unsalted sand (if possible, but not very critical).
Mix them all. First put a few smal stones (supllied from garden/park, etc) into the pot (make sure the pot has water drainage holes underneath).
And then fill roughly ¾ of the pot with soil mixture. Then place your plant/herb into the soil.
Then put rest of the soil mixture around the plant (make sure the roots are not left out of the soil or your plant is not placed too deep in the soil which covers the leaves) and then water it.
Place the pot where it gets light (but not directly) and air (but not cold).
Watering period: Check the soil with your finger; the soil should be always humid (neither dry nor muddy - overdose watering also harms the plant).
You can have same rosbery and laurel bay for years and years by the side of a small kitchen window. If you also learn how to prune them, they will live even longer.