You are starting way behind here, but I strongly recommend you hit up YouTube to get the basics on the Ruth Stout method and the Hügelkultur method.

I have modified both in the following ways:

First, I stripped away all topsoil. Whether you use or dispose of yours will depend on the availability of good topsoil in your area, and how good the current topsoil actually is. Then I dug down to provide myself with about 50cm (2-3ft) of vertical space to work with (accounting for the maximum height of the final soil level that I don’t want to exceed). If you aren’t doing this near a foundation, or you can still rework the soil to slope away from any foundation, you might be able to ignore this.

For the Hügelkultur method, I went with a flat layout instead of creating humps, and I used wood chips instead of logs and branches. I was aiming for a dense woody later that is laid down about a foot thick, and has about 8-12 inches of soil on top of it. This is meant far more as a decomposing layer that holds onto moisture, as I am in an area with sand and rocks further down that water just drains straight through. Bedrock might have this method as a good idea as well, just lay down an inch or two of sand before you put down the wood chips as a way of water running off if it gets saturated. And if possible, pack down the chips using a powered soil compactor, so you minimize the subsidence as the wood decomposes.

Once the topsoil is down, I finish the soil itself by bringing in several tons of horse manure, and rototilling it in. Horse manure because it doesn’t “burn” roots like steer/cow manure does. This is also why I went with an 8-12in layer of soil - so there is no chance of the rototiller reaching the wood chips. Also: June bugs and other root-sucking grubs love horse manure, be sure to spray with beneficial nematodes every year you supplement with manure.

For Ruth Stout (the soil cover), I have access to several acres of herbicide-free grass via a family orchard. I mow this through the year and pack it into a 8×4×4ft bin (this is fine for up to 1,000ft² of bedding cover, make it commensurately larger for larger gardens). Because I cut and pack when the grass is completely fresh and green, this starts the composting process that kills off any seeds, but the heat of the composting process also stops the process after a short while because I’m not turning over the pile to cool it off and introduce oxygen. This leaves me with lots of barely-composted grass clippings to use as an initial layer (about 60% of the total) when laying down the hay bedding. This suppresses weeds and holds in moisture much better than just hay alone.

You are likely to find green areas which are not treated with herbicide where the owners might permit you to mow and collect the grass clippings. Pretty much any green material, including heavily weed-filled areas, will suffice, as the seeds will be killed off during the composting stage. You want to avoid treated lawns because the herbicide will VERY negatively impact any vegetables you plant. In the end, you will be planting your garden through about a foot of thick hay and grass clippings; separate them by pushing them aside and plant directly into the soil. The grass and hay can also be considered as soil for bulbs and so forth, things like garlic can just be placed directly on top of the soil and re-covered. You will also have to recharge this layer every year by just putting more on top, do so in the early fall once you start shutting down your garden so you don’t disturb any beneficial insects that are bedding down for the winter.

Good luck.