erhaps the most obvious difference is that of the R sound like that in mother. The R is drawn out into an elongated pirate's ARRRRRRRRR. Don't elide your R! In a word like father it is not a lisped f-aaah-th-eh, it is f-aaaa-th-rrrrrrrr. The A is pronounced like apple and the R strongly enunciated producing (Mpg) (aifc) (au) F-aaaa-th-rrrrrrr. Likewise don't drop your H -- hither is h-ih-tth-rrrrr, not h-ih-tth-eh. Save your Cockney for Dickens.
The best practice tip for these is to open your mouth and exaggerate both the sound and the shape of your lips. Modern speech is subdued and BBC english arguably sedate.
These cheezy sound clips demonstrate some common pronunciations. I repeat the word in common english and then in elizabethan. These were taken off the built-in mike on a powerbook in 1994, so excuse the quality!
The most obvious of the pronunciations is the want sound, iterated over and over with words like: father, water, salt, and fall. Combining these next to hard R's twists the ear in a non-modern cadence. Here's a cheery greeting similar to the one I receive when I arrive home.