Question
could you please tell me the quickest and most effective method of lifting turf on an area of lawn that is to be replaced with beds. Lawn is 4-5 years old.

Answer
Quickest way is using big tool called a sod cutter.  It is a gas-driven device that strips off the first few inches of grass and dirt.  Its big and heavy, usually at over 300 pounds, so you'll need help getting it into a pick-up or on a trailer.  Check with your local rental yard.  They are pretty common items, and depending on the area size, it takes only an afternoon to strip up the turf.  

There are many other methods, less quick and effective, but still used if you want to save money.  Again, you said quick and effective.

Also, if you are stripping up turf with invasive roots like Bermuda grass, you'll have sprouts coming up even after stripping off the grass.  Let me know and I can suggest ways of dealing with that situation.

Good luck!