You should be able to get a reasonable steak stovetop using a cast iron grill pan, if you have a strong enough exhaust. Oil the cast iron pan (with canola or such), then heat it very hot, until it starts to smoke. Make sure the meat is completely dry on the outside (wipe with a paper towel, water will prevent browning) and gently place in the pan. Leave it there for a minute or two (it'll smoke quite a bit!), rotate 90° to get the nice grill marks. Leave for another minute or two. Flip, and repeat for the other side.
It may splatter, have a splatter screen handy. It will smoke, quite a bit, make sure the exhaust is on high.
You will probably have a medium-rare steak now. Using a thinner cut will make it more well done (you can cut a thick steak in half with your chef's knife, making two thin steaks); so will plopping it in the oven (not sure if you want the oven before or after searing, I like 'em medium rare...).
Remember to let the meat rest for 5 minutes or so before serving.
Also, if your steaks are coming out ridiculously tough, you're probably using the wrong cut of meat, or some terrible grade. What cut are you using?
[edit: I should note that, in case it wasn't obvious, the burner should be up pretty high]
Edit by rumtscho There is a reason this answer specifies a cast iron pan. If you are limited in your cookware choice, pay attention to the maximum temperature your pan can tolerate. If you are using a non-stick pan, you have to go on medium heat and wait longer, else you'll damage the pan. (And sorry, but you can't get it as tasty as on high heat that way).
If you are planning on eating a lot of the fat then you may go for grass-fed beef or similar animals as the slower growth can help with marbling and you'll get more flavor in the fat. Also get it from a butcher than will leave the fat on. Of course the fat will be part of the price point and if you aren't a fan of gamey meats you may want to stick with corn fed.
My personal preference is pork. Decent fat content and a very versatile meat for all kinds of dishes.
If you are serious about lots of meat and saving money then invest in a chest freezer and buy whole or partial parts of an animal. You'll get a large variety of cuts (you can have ones you don't like ground) and the price will average out across all the cuts. Search around for butcher/meat shops and most should provide you with a cut price list.
I usually get a pig or two a year. Has ranged between 2-4 dollars a pound depending on who I had raise it (cheaper usually if directly via butcher) and any smoking (bacon/ham), sausage making, etc I had done.
Best Answer
I've come across two great, and very different, types of steak. The first is typical in Argentina and is not aged at all, but from a young calf (6-10 months old), free ranging and grass fed (hence not like classic veal). This is really juicy, tender, and with a very "bright" taste. Good high-end Argentine restaurants usually serve meat like this, and in the UK you can order it from pampasplains.com, which I think is great.
The second is from an older cow and dry aged to tenderize, but the aging also gives it a deeper, more bone marrow-like flavour. The best I've had of this type was a cow from Limousin in France, served in Paris at a small restaurant called Le Sèvero (8 rue des Plantes, 14th Arrondissment, reviewed in the NY Times a while ago). It was amazing! In London, 32 Great Queen St's "Hereford beef" is a similar style and also excellent. They get it from a Hereford farmer called Tom Jones (seriously), who serves several restaurants.
Good steak should never be marinated in anything - all it needs before cooking is salt, maybe pepper if you like (though I sometimes eat it with Coleman's English mustard).
I'm fairly sure that grass-only feed is important to good meat, i.e. no cereal-based fattening-up, though it's hard to separately test this one variable. Breed also clearly matters (all Argentine beef seems to be Aberdeen Angus or Hereford). I love a nicely marbled, fatty steak like the ribeye, but my (Argentine) wife prefers leaner cuts like sirloin and filet - clearly a matter of taste.