I don't think the area would qualify as a 'meadow', since is is so shady that turfgrass won't grow. Woodland wildflowers would probably do well, especially if it is shady and damp and there is decent soil. And there are some shade-tolerant grasses that could be mixed in.

So, how do you get there from here? Tilling would probably not be a good idea -- it would damage tree roots and probably would not really kill off your grass. You could probably just plug plants in among the existing grass iIf it is very sparse. If there are no low-growing plants that you want to save, you could kill the turf grass with roundup (glyphosate) without harming the trees. Once the grass is under control, mulch the area and plug in plants through the mulch. It's probably not a bad idea to thin the trees, selecting the species or individuals that you want to keep. But be sure to learn what you've got before you do any wholesale cutting.

An area as small as you describe could be planted with natives pretty easily over a couple seasons. Many woodland natives will spread or re-seed, so you don't need to fill the entire area at once. Some good performers from my woodland garden are wild geranium, woodland phlox, woodland spiderwort, turtlehead, wood poppy, golden ragwort, woodland asters. Shade-tolerant grasses include river oats, bottlebrush grass, and various sedges. Ferns such as Christmas ferns and wood ferns are very nice additions. I don't know how many of these plants would be suitable for your area, although others on these forums will undoubtedly have suggestions.