Assuming you've identified which areas you want to turn into beds there are broadly 2 methods.

Method one, remove the turf. Manual labour and you're left with spoil to deal with but you can do reasonably intricate shapes.

Method two, lay a barrier over the top of the area to block sunlight from the grass. This will take long as you have to wait for the grass to die but the physical labour is greatly reduced.

Whichever method you chose, you'll then need to consider the soil underneath. If it's good, you can probably plant into it straight away. If it's poor (thick, heavy clay or weak, sandy soil) you will need to add some compost to improve it.

That's a very simplistic run down. I went with method one, I wish I had gone with option two because the effort and disposal of the removed turf was a pain, however the soil was so poor underneath that I had to do a huge amount of digging and stone removal anyway.

You could always look into the "no dig" method where you basically do method two but then just throw compost on top of the barrier you put down and plant directly. It's increasingly popular with gardeners.