I like to use the gourd when I am staying home and have time to prepare it properly, relax and refill as needed.
Most days though I put a couple of spoonfulls in a cup and add hot water, let it brew for a few minutes and sip through a bombilla (the metal straw with built in filter), I have enlarged the hole in the cap of a 14 ounce coffee travel mug that fits in a car cup holder, so that I can fit a bombilla and carry it when I go out.
I have never brewed in a coffee maker or used the tea bag, though I guess it should work.
The brands of Yerba that I use are what I find bulk in Mexico, mostly Taragui, Amanda and Nobleza Gaucha.
The traditional preparation can be complicated and probably varies by region, let me see if I can explain one way:
You fill the gourd with plenty of Yerba (1/2 to 3/4), cover it with your hand, turn it around and shake it a bit so that the powdered Yerba sticks to your hand (and you take it out to prevent it from blocking the filter in the straw), then you turn it back leaving the Yerba at an angle, most is against the side and there is a space where you put in some warm water, let it get wet a little bit and sip it, the first sip is somewhat bitter and some people spit it out, then you use hot (not boiling) water and fill from the empty side of the gourd so that some Yerba stays dry, put in the straw in the side of the water and drink, when you can't sip any more you pour in more hot water so that some of the Yerba that was dry gets wet, drink it and repeat the process until all of the Yerba has been used and the flavor is weak.
Traditionaly (at least in Argentina I believe) a group of guys gets together and one prepares the Mate, drinks the first sip, fills it again and passes it to one guy who drinks the second sip, he returns it to the first guy who adds water and passes it to a third guy, and so on until they go full round.
Another thing about the gourd is that is has to be cured before the first use, this involves cleaning, filling with water, scrapping the inside to remove the softer wood, then filling with a strong Yerba infusion and letting it rest for a day or more.
Hope this helps.
Luis
Edited to add: Geraldo, that's a really nice picture of fine Mate gear, thanks for showing, obrigado.