Leaves and stems:

Plants are prostrate, floating on the water's surface. Leaves are up to 1 mm long, stalkless, alternate and often overlapping, like shingles, along branching stems. A leaf is divided into 2 lobes and folded so the upper lobe is above the water's surface and the lower lobe is submersed. The upper lobe is blunt to pointed at the tip, somewhat succulent and covered in short, glass-like hairs, while the lower lobe is more membranous and rounded at the tip.

Stems are up to about ½ inch long, usually branched, with well-developed plants typically fan-shaped in outline. New growth is bright green to blue-green, often turning dark red later in the season, or having at least some red-tinged leaves. Plants can form sizable colonies, sometimes covering an entire pond, and may form multi-layer mats up to 1½ inches thick.

Spores:

Two types of spores are produced, in sacs called sporocarps: a male microsporocarp and a female megasporocarp. These develop in pairs on the lower leaf lobe, the pair being a single sex or one of each sex.

Male microsporocarps are globular and much larger than the egg-shaped female megasporocarp. Microsporocarps contain many tiny spores (microspores).

Megasporocarps each contain a single large spore (megaspore), much larger than the microspores. The base of a megaspore is rounded, sparsely covered in long hairs, and is pitted on the surface.

Notes:

What a cool little fern! If you ever pass by a pond that appears red on the surface, it may well be due to Mexican Mosquito Fern, formerly known as Azolla mexicana. In Minnesota, this species is primarily restricted to quiet backwaters of the Mississippi River, though it periodically pops up in other water bodies, and likely spreads there by waterfowl. It does not seem especially hardy and may not persist following winter freeze-up so don't expect it to be in the same pond year after year. There are 3 native Mosquito Ferns in North America and they can be especially difficult to distinguish when spores are not present; a microscope is generally required to see the identifying characteristics in either case.

In Minnesota, the only similar species is Carolina Mosquito Fern (Azolla caroliniana, a.k.a. A. cristata), which has megaspores with a smooth surface, not pitted, and is more densely covered in long, matted hairs (Ferns of Texas has a photo of that for comparison). It is also said to rarely produce spores where A. microphylla frequently does. The general consensus is the real distribution of these two species, in Minnesota as well as nation-wide, is not precisely known since many collected specimens lack the sporocarps that are needed for a positive ID. It is possible the more cold-hardy A. caroliniana is actually more common in Minnesota than A. microphylla, though it's only been recorded once in the state, in 1946. Time will tell.

Fun fact: the common name “mosquito fern” is said to come from the notion that this plant makes such a dense covering on the water's surface that mosquitoes can't breed. Nice idea, but unfortunately false. Mosquito Ferns also have a symbiotic relationship with nitrogen-fixing blue-green algae, which may be found in cavities of the upper leaf lobes. It's an especially important green manure (fertilizer) crop in rice paddies, used heavily in southeast Asia and introduced elsewhere for agricultural and horticultural purposes. Mosquito Ferns are also considered invasive species in Japan and Great Britain, and another species (A. pinnata) is listed as invasive in Wisconsin. Such is the price we pay for moving stuff around the planet.