The name, the story, the myth
Many of the celestial constellations born during the 17th and 18th centuries celebrate the progress of science, so it should not be surprising the name given to this constellation, Microscope, wanted by Nicolas Louis de La Caille, who introduced it in 1756, certainly showing himself well descended in the spirit of the Enlightenment, naming the stars taken from the tail of the Southern Fish, to an optical instrument decisive for the developments of experimental research. The original name Microscope was then replaced by the Latin name of the object, Microscopium.
It remains rather incomprehensible the will of the abbot to create this constellation, to make a cut and isolate a group of weak stars in a separate constellation, it is not apparently the purpose to highlight something relevant.

The map of Stellarium with the Microscope
It is a constellation whose three brightest stars do not reach the 4th magnitude, while all the others are obviously even weaker.
From the celestial map of Stellarium, we can see that this small constellation is located between Sagittarius and the Southern Fish, just below Capricorn.
To be able to see some of its stars, we need very dark skies, like for example in the mountains and then we can look for its few weak and elusive stars in an area of sky poor of bright stars and very low on the horizon: it is located halfway between Fomalhaut (α PsA) and the famous Teapot (modern asterism and very comfortable, apt, inside Sagittarius).
Given its location and the particularly difficult observability conditions, being able to locate it is certainly a great success!
As we will see, the constellation has a couple of nearby stars, a pretty big star and just a couple of deep sky objects.
The Microscope is a recent constellation, created by Lacaille subdividing the Southern Fish constellation. The only representation of it can be found in Stellarium, which represents the well known precision optical instrument in a not modern version.

Two nearby stars
Inside the constellation there are two nearby stars: the first is the variable AX Mic (also known as Lacaille 8760 and HIP 105090), a 6.7 star, class M2 and located at a distance of just 12.87 to our Sun: its makes the star in question the brightest reddish-orange dwarf in the whole firmament.
My Aicsesi friends are very proud of this fact, and they immediately sent me the photo of our Sun, which from their parts appears to be 2a in an area of sky full of stars of the Big Dipper and near the Castore and Pollux twins and Raccoon. They are, yes, proud of their star, but not of a detail of their physical appearance on which obviously they never speak: not by chance from the name of the constellation the poor people are also called the Microscopic. But let's cut the nonsense and talk about the other star next door.
It is another variable, AU Mic, also known as HIP 102409, this time of 8.8, class M1, placed at a greater distance, equal to 32.32 al.
My friends live in a small planet rich of felines and they have been very happy to send me the photo of our yellow dwarf that this time is barely 5a , placed in the same zone of sky seen before, where now Sirius appears too.
A big star

From the diagram of comparison of the stars of the Microscope with those decidedly bigger and known ones (realized by the undersigned with Illustrator) we can see that inside the constellation there is a quite big and bright star (of 5.5) , η Mic, of spectral class K3, an orange giant: as we talk about this spectral class, the illustrious representative like the famous Aldebaran cannot not immediately come to mind.
Also in this case the star of the Microscope is bigger (39 times our Sun) than the star of Taurus: it is not as well known and bright, since it is at a good 712 al here compared to Aldebaran, which vice versa is much closer, placed at only 66 al.
Deep sky objects
As said before, inside the Microscope there are a couple of deep sky objects, two galaxies.
The first one we see is the barred spiral galaxy called NGC 6925.

the barred spiral galaxy NGC 6925
while the second is the spiral galaxy NGC 6923

the spiral galaxy NGC 6923
Names of stars and visibility
Given the scarcity of bright stars and the young age of the constellation, none of its stars received a name.
As far as the visibility of the constellation is concerned, at the usual time of 9 p.m., it is low on the horizon, south-east, in the second half of August, culminating in the south in the first ten days of October at about fifteen degrees on the horizon, and then low on the horizon, south-west, in the first ten days of November.
Good observations!