The mate is the "cup" (in Argentina, it's pronounced "ma' tay"). The inside is often made of a type of a gourd and the outside is often leather. Some are made entirely of wood. No doubt, there are other types also. The tube is called a bombilla (in Argentina, it's pronounced "bom bi' sha"). It's a high quality straw with a filter.
See a picture of Mark in Argentina drinking Yerba in his newly cured Mate: www.markrice.com/0305argentina/ar_images3/36110054_MarksFirstMate.jpg
Yerba is a type of tea in Argentina. It's steeped in tradition. I was honored when asked to take part. The taste of yerba is bitter. Many use sugar, orange peels, different types of tea, and other ways of flavoring. However, many drink it in it's plain form. I learned to like it very quickly, in part, because I like bitter tastes, like good black coffee. If you dislike bitter tastes, you should try it with sweetener and other types of flavors.
Before use, a gourd type mate should be cured. It takes about three days (I like to cure it for longer than that). You can likely cure it with other "bulk" teas also, although they may will give the mate (cup) a different flavor. That's not necessarily bad. Use another kind of tea if you want. Here's how to cure:
Preparing to Drink
Put the yerba in a cured mate (see above for curing) until it's about 70% full. Place your hand over the mate, turn it upside down and shake it so the smaller particles fall toward the rim (toward your hand) and the larger particles are at the bottom of the mate. Turn right-side-up. Pick one side and poor very warm water (not hotů if the water is cloudy, it's likely too hot). (Always poor the water in this location so the air can escape through the dryer side.) Once the water has caused the yerba to raise a little, you can insert the bombilla (filter end down) into the yerba, trying not to disturb the yerba much.
At this point, some people suck out the first serving and spit it down the drain because it's both strong and has small particles. The subsequent servings will not have as many particles because the larger pieces begin acting as a filter, helping the bombilla to filter. However, some people drink this first portion. Refill with very warm water and hand the mate to the first participant.
Mate is not sold in restaurants. The idea sounds funny to the people of Argentina who use it. That's because it's a very social event and is intended to be shared among good friends and family. I consider it to be an honor if people ask me to take part. There is much socializing done during mate. The closest analogy I can think of is a coffee break where people talk for 20 minutes.
There is a server who has the hot water the yerba and the mate. The mate is filled with very warm water, then handed to the first participant. That person drinks all the tea, then hands it back to the server, who refills it with very warm water, and hands it to the next participant. Everyone uses the same bombilla and the server is traditionally the only one to refill with water.
It's a great tradition. Then again, I'm biased because I love South America.