What is the best way to level an existing playset with only one person?
Seems like there are at least three questions here: how to temporarily support the structure so that work can be done, what materials to use for shimming the low points, and how to figure out where to add or remove materials (and how much).
Temporary support
It's tough to install a good base or to make adjustments when you've got something already sitting on the ground. Elevating it off the ground just takes a little creativity and resourcefulness. You might already have some kind of jack around the house (or a desire to buy one): a bottle jack, a floor jack, a tire-changing jack buried in the trunk of the car.. You may need to add blocks of wood to support the jack on the ground and/or to help the jack reach the play structure. Have some kind of cribbing material (more pieces of wood, usually) on hand to support the structure while it is raised.
Even a shovel or and a rock or block of wood as a fulcrum can work to pry something up an inch. A method I especially like is the &quot;2x4 jack&quot; as explained in this youtube video.
Foundation/support material
This depends a lot on what materials the play set is made of, how large the surfaces are where it bears on the ground, and how good your soil is for supporting the play set. Not knowing details about any of those things I'll give general ideas. Bricks make a nice support. Many home centers carry precast blocks and pavers in various shapes and sizes; some of these might be a good fit for your project as well. Finally, 2x4 or 4x4 pressure-treated wood cut into blocks of appropriate sizes might be useful.
It may even be fine to support the structure directly on the bare soil. In this case you can simply dig down the soil in the high areas or add soil, rocks, or bricks/blocks/whatever in the low areas.
What's level?
If you begin by finding how far out of level the ground is now you can make better choices about whether to dig the high parts down, build up the low parts, or do a combination of the two.
A water level is a pretty simple and inexpensive way of leveling points over a relatively large area, especially where obstructions make the use of a string and/or straight level impractical. There are fancy little kits for this, but all you really need are a bucket full of water, some tubing, and a measuring tape. Only the last few feet of the tubing has to be transparent (but all of it can be). The basic idea is that one end of the tube is placed in the bucket and the bucket and tube are filled with water (remove air bubbles from the tube). The far end of the tube can be moved freely around the site; the elevation of the water inside the tube will remain constant. Measure the distance from ground surface up to the water's level. Whichever point has the least distance to water level is the highest; the point that has the greatest distance is lowest; the difference between the two numbers is the difference in elevation.
That's probably not enough words to make a really clear explanation.. but I'm sure there must be a few youtube videos which will make it clear!