Hmm, do I have any USEFUL ideas? That is harder.
Crush eggshells before adding them. In my heap, they break down very slowly and stay birght white. Then they stand out and do look like garbage. You don't need to wash them: egg white is a great "green" and your composting critters will lick it right up.
>> What other cheap ways can we do to prepare our soil for healthy gardening?
Can you get free manure from someone, or get into a fruit stand's dumpster? Buckets of coffee grounds from a coffee shop or 7-11?
Make sure that patch drains, or at least that it is not at the bottom of a low spot. Roots need to breath or they drown and the plants die. If the root zone fills with water, it has no air.
First, what kind of soil? If it is sandy, add things that will hold water. If it is sandy, you have fast drianage or too-fast drainage, and most of my experience will be4 irrelevant to you.
If clayey,. help it to drain by adding organic matter and coarse amendments. Do you have access to free sandy sub-soil? Clay is especially needy of compost.
Usually I think soil that has never been gardened in is probably too compacted. Dig it up to a depth of one or two shovel blades, depending on time and energy. Break up big clayey chunks. Add as much compost as possible. if you had an unlimited budget, add 'amendments" like grit, bark fines, coarse sand or whatever. Mix it with a shovel or a pitchfork, trying to mix everything and break up clods into small bits. Rake out roots and the larger rocks. Gravel and things smaller than 1/2" or so won't bother the roots.
The goal is to reduce it to fairly fine particles and "fluff it up" as much as possible - creating loft and air spaces within the soil. Happy soil will have something like 5-15% "open voids" that can be filled by air, or briefly filled by water that must then mostly drain OUT so that air can come back in.
Then, with enough compost and enough water to be slightly moist, you can tamp it just a LITTLE bit to firm the particles together into clods or peds with some air space left between the particles and clods. That's 'structure'.
NEVER WORK THE SOIL LIKE THAT WHILE IT IS WET! That breaks down any "structure" that it had and allows it to settle down and compact itself 100% into mud or "pudding" with NO air spaces. That won't grow anything, and it takes a LOT of work to correct. When ti dries out, it becomes like concrete.
I did that once: dug and forked too soon after a rain. That soil did not recover in the year or so that I continued to have access to that area. At least it was all weeds before I came, so I didn't destroy someone else's garden.
Work the soil while it is fairly dry, or no more than a little damp. Squeeze a handful as if you were making a snowball. If it "clumps" and forms a ball, BEWARE. It is too wet or too clayey. Let it get drier before you break it up finely.
If you try to make a snowball, and it falls apart in your hand without even needing to be poked, God smiled on your yard and gave you soil that was not too clayey.
