This is a technique I developed a few years ago that is fast, inexpensive and attractive. The materials you need are: wet newspapers, a trowel, a bucket of compost, an empty bucket, seedlings, and a bale of hay/straw.
Step 1: Lay out newspaper on the lawn as explained in the previous post, and cut a capital H in the wet newspaper with the trowel.
Or a capital I if you prefer.
Step 2: Fold back the paper like opening French doors.
And dig out the sod and soil to the volume of a 1 litre/quart yogurt container. Carefully put the soil into the empty bucket so as not to allow weed seeds in the soil on top of the newspaper.
Step 3: Fill the 1 litre/quart hole with compost.
Step 4: Plant the seedling, water thoroughly, and fold back the newspaper.
Step 5: Mulch with hay or straw.
* Note that we don't buy in hay or straw because we use tall grasses that we cut with a scythe and harvest with a rake. I have used wood chips as a mulch on one job, but that was only as a very low-budget approach in that particular case.
With a stack of newspapers and a few bales of hay/straw you could convert an entire lawn to garden in a weekend.