Shake it up baby!
There are scores of designs of cocktail shakers, many of which come as a set containing everything you need for making a great cocktail.
My fave among the countless cocktail shaker kits out there is this one from Libbey. There is a 20 ounce glass mixing glass, a stainless steel shaker, and a stainless steel Hawthorn-style cocktail strainer. It is dishwasher safe, although hand washing is recommended. Beware of any glass with painted on letters. Machine washing will eventually fade or remove them. But hand washing doesn't damage them at all.