How to pronounce 儿 in conjunction with other characters
Wikipedia has a very useful page on Erhua. I don't know how to type IPA here and I'm not sure whether the OP knows IPA, so I'll summarize the rules informally here, writing the approximate erhua pronunciation inside quotations marks. (Note that this does not represent the pinyin spelling of erhua words; those rules are different.):


Final i and n are deleted: 把儿 = ba + er -> "bar"; 伴儿 = ban + er -> "bar"; 盖儿 = gai + er -> "gar"
Main vowels i and ü are retained, and the "er" sound is added at the end of the syllable:  气儿 = qi + er -> "qier"; 劲儿 = jin + er -> "jier" (the n is deleted by the above principle); 裙儿 = qun + er -> "qüer", 驴儿 = lü + er -> "lüer"
Certain vowel sounds merge. These rules are complicated; I refer you to Wikipedia for more details.
Final ng is deleted, but the vowel becomes nasal. I've left this rule until last because (as a native English speaker) I find these sounds difficult to pronounce. Wikipedia, or the sound files mentioned in other answers, will give you a better sense of how these vowels sound.