You need incense charcoal (the best are the Japanese brands, but whatever you find in the store marked as incense charcoal will do).
You need a heatproof surface. Any bowl will do if you add a layer of sand or ash to insulate it from the heat of the charcoal; otherwise, I advise you to stick to metallic bowls, censers, cauldrons, etc,. on top of a trivet or some other heat resistant surface. If you do burn initially on bare metal, I suggest saving the ash. After a few uses, voila! a do-it-yourself layer of insulating ash, and then you can put that trivet away and burn the incense in nearly anything you want to.
A metal burner doesn't have to be anything special unless of course you want it to be special: on a few occasions I've used a stainless steel condiment/prep cup (
http://www.crateandbarrel.com/family.aspx?c=670&f=7901 ).
You probably do not want to spend $$$ on the tiny packets of (usually low quality, in every sense of the word) resin at your local new age shop. It's not the local owners who are at fault for this, it's the unscrupulous suppliers who take a product they buy at $5- $10/ lb and repackage it in tiny, grossly overpriced packages they then distribute at wholesale to small shopkeepers who don't have the volume necessary to order from the botanical distributors.
Look around for a better source. I often like to buy my frankincense from Eastern Orthodox supply houses-- the prices are far lower for much, much higher quality incense that doesn't come with a sticky coating of greed and exploitation all over it. One source I've used is at
http://www.orthodoxsupply.com/incense.htm (Note: the myrrh "fragrance" that place sells is not genuine myrrh but some neutral resin base, probably benzoin, infused with myrrh essential oil. The same goes for the other products listed as fragrances. They are good products, but unlike the frankincense, they aren't the real thing).
I last found some excellent myrrh at a reasonable price on eBay, but there are quite a few suppliers, both brick and mortar and online, who sell myrrh at a reasonable retail markup (which should be somewhere around $25/lb, more or less depending upon the quality). Look for places who deal in herbs in bulk. They often carry incense resins, especially myrrh as it has medicinal uses.
You can, and unless you are censing down a very large area, probably should, break the charcoal blocks into two or even four pieces. Otherwise, you'll end up burning half the brick to no purpose other than to slightly increase your carbon footprint.
There is a trick to getting the best results when burning incense on charcoal. Just
barely ignite the block, so that sparks fly (if you're using "self lighting" charcoal) but you don't see any obvious glow. You want the charcoal to burn cool. That allows you to melt, rather than burn, the resin, giving a better, longer-lasting scent. Getting it lit just so is a matter of trial and error and experience, so don't fret if you don't get it perfect right away. As long as the charcoal is lit, you will have smoke.
Don't try to light charcoal with a match. It takes more than a match to get it going. Light it with a lighter or similar device, or with a candle (
not one you're using as part of a ritual, but a separate utility candle).
Frankincense is a fire incense, ruled by the sun, myrrh is a water incense, ruled by the moon. Frankincense has a very nice scent when burned on charcoal, myrrh, not so much. Of course, if what you're doing doesn't require that kind of solar/lunar, fire/water balance, you can simply burn frankincense, which in and of itself is a perfectly fine purification incense. Or you can go heavy on the frankincense when blending, or you can use additional ingredients when compounding an incense which can mask the not-so-great scent of burning myrrh. Of course compounding your own incense gets complicated fast, so consider the above suggestion as applicable only if you're in the mood for learning some complications ;)
Unless you are actually getting complicated, there's no need to grind the resins to powder. Just pick out a few pieces and put them on the lit charcoal. One or two tears of each resin ought to give you plenty of smoke.
There is of course a completely different way to use these two resins (and for that matter anything else with a scent), and that's to simmer them on the stove. Myrrh smells quite good when simmered (I guess one could say that, when simmered, it comes into it's own element ;) ), as does frankincense. I wouldn't use that method to chase away bad stuff, but it works well to support an already clean environment.