I see you’ve gotten some good answers from a British English perspective, so I’ll go ahead and provide the American perspective.

First of all, there may be some confusion as to what you meant by “rolling your tongue.” A “rolled R” is synonymous with a trilled R (“roll” as in “drumroll”), that is, an R where the tongue vibrates multiple times in the mouth. As Chris says, this rolled R is only used in Scottish accents nowadays. On the other hand, it is indeed true that the tongue should be curled up a bit (but not as much as in Mandarin — especially the tip) for a standard R in English.

For an American R, you will definitely need to use your tongue, because labialization is just a co-articulation. The tongue base should be retracted (pulled back) and so should the tip (but not too much). For the R, the sides of the tongue are raised to the roof of the mouth and the air is allowed to flow freely over the middle of the tongue. For the L, it’s the opposite. 

Labialization: This is optional, but it is typical of General American as well as RP (so-called standard “British English” pronunciation). For a syllable-initial R, simply round your lips a bit (if the following vowel is rounded already, you don’t even have to do anything special). The  labiodental articulation Su.Ki. and Mr Peachey describe is a feature of proper RP, and may also be heard on the US East Coast, but would sound strange in most of the US. In any case, I agree with Peachey that when you get the R to sound more native, “you'll find that a lot of words suddenly become much easier to say.”