How can I cheaply cook a bratwurst that is similar to a grilled brat with only access to an oven or stovetop?

Most ovens have a 'broil' setting (where the top element is on, and not the lower element).

You'll likely want a 'broiler pan' so that you can drain the grease away from the food (and catch it so it doesn't light on fire). They're under $20 online.

1. Set the rack of the oven so that the food will be about 2" from the upper heating element.
2. Heat the broiler on its hottest setting, but leave the door to the oven open.
3. Place the food in the oven, but again, don't close it.
4. Turn the food occasionally until it's cooked to the level you want.

As for the bit about not closing the door : If you close the door to the oven, it might heat up too much, and shut off. You need the element actively heating, so that you have radiant heating, not convection or conduction. (this is also why you want the food really close to the heating element). Note that this is for electric ovens -- I don't think gas ovens have the same issue.

If you cannot splash out on a propane barbecue why not use charcoal? There are plenty of options there, you can pick up very simple bucket barbecues for very little money, and in my personal opinion you get much better flavor from charcoal than gas. For brats a disposable charcoal barbecue will give you decent results, and they are pretty inexpensive.

Look at local yard sales and classified ads, you'll see someone selling a decent used barbecue at some point, gas or charcoal.

If these aren't options and you do have a broiler (aka grill in some parts of the world) in your oven then use it as @Joe suggests, you'll get the closest thing to a bbq. If you don't have a broiler then pick up a grill pan and use it on your stovetop. I like to keep a cooking torch handy to touch up the areas that haven't been browned. You can get a plumber's torch at a hardware store, it's the same thing.

This started as a +1 comment to GgD's answer, but it's too long, so I'll post separately.

I agree with GgD: Buy a charcoal grill. You can actually have a "grilled brat" with better taste, for less money than gas. A quick internet search shows small charcoal grills selling for as low as $15-20. And you can do a perfectly fine job grilling on even the cheapest charcoal grill -- it really is just a metal box with a hole in the bottom and a hole in the top, with two grates (one for the charcoal and one for the food). You could actually make a makeshift one yourself if you have a couple metal grates lying around, but for $15-20, I'd just go buy one.

Charcoal itself is very cheap as well. I personally prefer the "natural lump" charcoal for flavor, and you can often get a large bag for $10 or so. (The standard briquets are even cheaper, and they'll do fine if you're really on a budget.)

Also, skip the lighter fluid and use a charcoal chimney for easier lighting and even more savings without the chemical aftertaste. They often sell for $5-10 at a store, but if you have a large empty can, you can easily make one at home for $0; instructions can be found online.

The only disadvantage to charcoal is the extra time (15-30 minutes) it can take for charcoal to light and heat up. And it has a somewhat steeper learning curve than a gas grill. But once you've done it a dozen times or so, you'll have at least as much control as a gas grill (and arguably more in some situations, like when you want temperatures outside the "high" and "low" range of the gas burner, or when you need to move your heat source around dynamically while cooking).

Lastly, in terms of cooking technique: put your hot coals on one side of the grill; even with a very small, cheap charcoal grilll you can have a "hot side" and "cool side." Brats usually like to have a longer time over indirect heat on the "cool side," so the interior can heat and the fat will liquify, producing a juicier result. The longer time on the grill will also absorb good "smoky flavor" from the charcoal. If you like, sear on the "hot side" at the beginning to get that crispy skin as dark as you want.