Professionally trained detailer with years of experience here. Ultimate polish is formulated from their Mirror Glaze #205. It is not a wax, so you don't want to let it dry then buff. Instead, it is a minimally abrasive polish using their SMAT abrasives. Basically, polish not wax is what makes paint shine. The wax is a protectant. This product can can cut out some light swirls especially in soft paint but like any polished it has to be worked against the paint. Although it can be used by hand, the proper tool is a Dual-Action polisher known in the industry as a DA. Basically, you might get 5% of this product's capabilities by hand, but it will really come alive if you get a DA.
I would recommend a Porter Cable 7424 XP or similar polisher because they are inexpensive, have a shorter 8mm orbit, so they don't create much heat to warp the pads, and they still create lots of paint correcting power. Being free spinning, it is forgiving in that if you tilt it the pad or run it up against a body line it stops rotating instead of burning the paint.
When you get such a machine, I recommend the 5" Lake Country backing plate (make sure to use the fiber washer between the backing plate and machine), and the 5.5" pads. The backing plate it comes with is junk. Get a couple of the Lake Country White pads for now because they are perfect for polishing, which is what you are doing. Draw a mark on the yellow backing plate with a black marker as a visual (more on this later)
Now watch some Youtube videos. But essentially, get the pad damp with product the you need a couple pea sized dots of the product. Now spread it out on low speed like 1 or 2... over a 2' by 2' area. Next crank the speed up to 4 or 5 (I even use 6), and press down hard (usually 10 to 15 lbs). You will hear the OPM change of the machine as it gets loaded, and the foam disc will slow down. Watch that mark. If it gets too slow or stops rotating, you are pressing too hard. If it free-wheels you need to press down more. Now make slow passes in an S shaped pattern keeping it flat and slowly creap it across the area you are working. Do about 4 to 6 passes. Wipe with a microfiber.
Examine paint and if you like what you see, repeat over entire car. At any rate, this is how to use Ultimate Polish. Watch some detailing videos by Superior Shine, Auto Fetish Detail, Mike Phillips /w Autogeek and Show Car Garage, etc. Also watch the Megiar's folks like Jason Rose, Mike Stoops, Mike Pennington etc. There are a ton of folks who polish paint. Watch the speed the move and judge how fast their DA backing plate is rotating and how the machine sounds. Replicate the pressure and arm speed.
After you do this, you might consider buying a finishing pad to apply your wax (use a slow speed like 2), and you may want to buy a cutting foam pad and something like Ultimate Compound to tackle much deeper scratches up to theoretically about 2000 grit sanding marks. When you learn more, you can get different backing plates, pads, pad types, compounds, and polishes. That said, Ultimate Polish is about the best Consumer-Grade polish I have ever seen. It's like 205 but with even more open work time, even easier to wipe off, and it has only slightly less cut (probably about a 3 on the Meguiar's scale where 205 is a 4). Either way it finishes super nice and glossy. What it and also 205 won't do is remove deeper defects. It is purely to remove haze and make brilliant and glossy though on softer paint it it may remove swirls. Just try it to see what it is capable of doing.
