What is the best process for transforming part of my lawn into raised garden beds? I used to have strawberry plants with a few dwarf trees in this area but after fighting the grass for years, it finally took over the area, so I'll need to start from scratch.

The simplest means of transforming a lawn into a garden is to lay newspaper or cardboard over the grass and cover that with a mulch (I prefer shredded leaves) both to hide the paper and hold it in place. Depending on when you do this it may be a few weeks to a few months before the bed will be ready.
So what kind of soil do you have there around Sacramento?

Soonerman....(you live in Oklahoma?)

To want your strawberries to grow in a raised bed is a wise choice. Strawberries need a place that drains well.

As far as selecting the site you wish to build your raised bed, start by removing the grass, either by renting a machine to lift the sod, or with an edger, cut strips, then roll up the sod.
Use this either to replaced plugs elsewhere in your lawn or turn the sod pieces ---green side down...in your compost pile.

Measure out your sized bed and then till the area with a roto-tiller down at least 12"...18" to which you add lots of organic material, and some coarse builder's sand.
Peat moss can be a large part of your mix since it is wished your ground be acidic for the strawberries that grow well where the pH of 5.5 - 6.5 is ideal.

A soil test you might wish to get to affirm this pH reading. If the pH is below that...you will have to add some dolomitic lime to raise it. If it is not sufficiently near the 6.5..you can add some garden sulfur according to the directions on the label.

As part of mixing the peat moss with the soil, use hot water to make it easier to handle.
The area must have a well-endowed organic make-up to properly hold moisture and give nutritien to the plants.

I assume you know the berry plants best for your soil. Do keep in mind strawberries must have lots of sun and are planted in early spring.
Use straw for mulch.

How you make your raised bed is up to you....but it needs to be built as soon as your weather allows it.

If you think this might be a bigger job than you wish to tackle, strawberries can be grown very satisfactorily in containers. Large containers are available at garden centres and just make sure the organic make-up of the soil is as the raised bed would have been.
The containers must drain well.

You can even have strawberries hanging you can use the same soil you would for them, but they can be grown in panty hoses, just cut off tops and secure to something strong to hang them on fill with dirt cut holes, put plants in from top to bottom, the plants will attach to the hose and it looks pretty when they bloom. I do vineing plants this way to.