If you haven't done this before, there will be a learning curve especially with regards to aseptic technique. Everything will need to be sterilized properly or you will wind up with contamination and the process will fail.

Usually you can take a chunk of the existing spawn and put it in a new spawn bag to start the process all over again. Results will vary greatly depending on how dried out the spawn is and how dirty (with other microbes) it is. You can also use tissue from the inside of the mushroom (typically from the stipe but oysters don't have much of a stipe) on malt extract agar to grow mycelium on plates. This can then be chopped up and put into spawning bags, jars, or just more plates. Some people make a liquid culture out of the mycelium but agar seemed easier to me so that's what I do. Spore prints are "easier" in the sense that you are less likely to get contamination than with a mycelium culture, but they will generally take longer and there's a chance you wind up with a strain that doesn't fruit as well.