Ceiling holes are rarely uniform, and if you attempt to patch an uneven area, you'll be creating more work for yourself. It is simpler to cut away a larger portion of the ceiling that is square or rectangular in shape. Use a utility knife and carve around the hole. Expose a portion of one of the ceiling joists so that you have a solid surface to attach the new patch. This eliminates potential ceiling patch collapse issues.
Measure the area that you cut and use this to create a template for your new drywall. Lay the template over the drywall and cut it to fit with a utility knife. While you can just measure and cut the drywall directly, having a template makes it much easier to get a straight edge and helps you get the exact amount you need to avoid trimming or having to cut a bigger piece later. Insert the patch into your ceiling hole and drill it into place with drywall screws.
Before you can use spackling compound on your patch, you need to tape off the edges first. Scrape off the texture on the surrounding ceiling and apply your tape. Now you can spread your compound over the tape and blend it in with the rest of the ceiling. The entire patch can be covered with compound, but do not over-apply or you run the risk of putting too much weight on the drywall.
Once the spackling compound has set, the patch needs to be matched to the rest of the textured ceiling. Instead of renting a hopper, use a spray can texture. This is well suited for a smaller area and reduces your costs. Spray the texture over the patched area lightly. Slowly build up the layers of texture on the patch until it blends seamlessly with the rest of the ceiling.