What comes immediately to mind is say ’Bras-spung and Bkra-shis-lhun-po for Drebung and Tashilhümpo respectively.
I'm not at my home computer, otherwise I would type your Wylie out in Tibetan Uchen...but anyway, here goes:
Tibetan is written left to right, like most Western scripts, but also vertically, as well as horizontally. In other words, letters can get "stacked" atop each other.
In the case of 'bras.pung, the apostrophe represents a small "a", which is a prefix letter, with no real effect on pronounciation. "Ba" is subscribed with "ra," or "Ratak" (literally the "tail of Ra," or the bottom half/stroke)...this combination is pronounced as a cerebral retroflex, which sounds to our ears like "Dra." Now, the vowel is lengthened from "ah" to "Ay" sound due to the silent "sa" (much the same way our English "silent e" can lengthen a preceeding vowel...).
So, your first syllable is pronounced "Dray..."
"Pung" is easier, as there's no stacking...simply "pa" with a "u" vowel marker called Shabkyu underneath, and a final Ng.
The "Pa" sounds a lot like our "B" though I find it to be more precisely halfway between an unaspirated "p" sound and a round, labial "Ba."
See? Easy, right?
I'd recommend a teacher.....learning the script doesn't take long at all, once you know the rules. Reading at any speed takes practice. And grammar and vocabulary take time and practice.