With a very good light microscope, the smallest thing that can be seen is about 500 nanometers big. One nanometer is the one-billionth part of a meter. This means that you can see objects that are about 200 times smaller than the width of a human hair.
Bacteria can be about 1000 nanometers big, which means you could see them with a light microscope. To inspect objects even smaller, you would need an electron microscope that accelerates electrons, shoots them through your sample and measures their transmission. Such a microscope is called a transmission electron microscope and the best ones can resolve up to 0.05 nanometers. This length scale is so small that you can see single atoms with it. So you could look at your bacteria, zoom in further to see their membranes, zoom in to see the protein that builds up their membrane and zoom in even further to see the atoms that form these proteins.
The smallest object or distance that can be resolved (distinguished as unique) with a microscope depends on the type of microscope. This is because microscopes work essentially by bouncing particles off of (or shooting particles through) the object being viewed and then catching the particles on a detector.
With a visible light microscope (the standard optical type in middle/high school science labs), which uses light in the visible part of the spectrum, objects down to about 10-7 m (= 1/10000 mm) can be distinguished. This is roughly the size of cell organelles. To resolve smaller requires the use of electron microscopes.
As the name suggests (electron microscopes), these direct electrons, rather than light, at the target. With an electron microscope, individual atoms can be resolved. Atoms are roughly 2*10-10 m in diameter, or about 1000 times smaller than the smallest objects resolvable with a light microscope.
The resolution limit of a microscope is determined by the wavelength of the "stuff" that is being used to illuminate the target. The object must be more than 1/2 the wavelength of the illumination source in order to be clear. As a crude example of this, imagine trying to "see" a pack of playing cards on a table by throwing "particles" at it and watching how they bounce. Now imagine using a beach ball as the particle. If you hit the cards, the ball will extend beyond the edge of the deck and hit the table, so you won't really be able to tell where the edge is by the bounce. Even with a direct hit onto the deck, the table will greatly influence the bounce, and you won't be able to determine very precisely where or how big the cards are.
Now imagine using a marble as the particle. The marble is much smaller than the beach ball, and more importantly is smaller than the cards. Hitting the cards with the marble will not have any interference from the table; you will be able to tell very well where the edges of the cards are.
Imaging with light vs. electrons is similar. In a light microscope, the "stuff" is light, which comes in discrete pieces called photons. In an electron microscope, the pieces are electrons. There is some quantum physics involved, which is far beyond the scope of this question, but essentially the photons seem bigger than the electrons when used in a microscope, just like the beach ball is much bigger than the marble. Although both photons and electrons are commonly referred to as "particles", both exhibit what is known as "wave-particle duality". This means that they are not particles and also are not waves, but rather display properties of both. One consequence is that both "particles" have a wavelength. The wavelength of any particle is given by the de Broglie relationship: L = h/p;
where L is the wavelength, h is a number called Planck's constant (h = 6.626*10-34 m2-kg/s), and p is the momentum of the particle. For particles with mass (such as electrons, but not photons), momentum is given by p = m*v;
where p is momentum, m is the mass, and v is the speed of the particle. Putting in some numbers for electrons (m = 9.1*10-31 kg, v = 1.8*108 m/s) gives a wavelength of 3.8*10-12 m.
On the other hand, visible light has wavelengths of around 400*10-9 m. Since the wavelength of the electron is so much smaller, the size of objects resolvable with an electron microscope is much smaller than those that can be seen with a light microscope.
An aside - photons do not have mass. However, their momentum can be found from their energy via E = p*c and E = h*c/L,
where E is the energy and c is the speed of light (and p, h, and L are still momentum, Planck's constant, and wavelength). Usually this isn't needed to calculate wavelength though, because the wavelength of light is known/specified.
Allegra, that is a fantastic question! The smallest thing you can see in a microscope depends on what type of microscope you are using. In general, the smallest thing you can observe (also known as the diffraction limit of a microscopy system) is given by a simple equation:
d = λ/2 where d is limit of resolution and λ is the wavelength of the type of wave/particle you are using in your microscope.
This equation is important because microscopy relies on the interaction of light with the item you want to observe. As the item being observed becomes close in size to the wavelength of light you are using to observe it, the image can't be resolved as well, making it blurrier.
With a traditional microscope, you are using light that is in the visible wavelengths and therefore, the smallest things you could possibly observe would be around 190 nanometers in size. Many other things can be used to microscopes though! For example, one can use x-rays, which have far smaller wavelengths than visible light which allows for observation of much smaller things. Electrons can be used for microscopy as well, allowing for even greater precision.
In the end, there are fundamental limits to the smallest things you can see with microscope, but they depend on the type of microscope and what medium it uses to create the image you want to observe.
The answer to your question really depends on the type of microscope you are using! A regular microscope, the kind that you might look through with your eye, will magnify what you are looking at by at most 1000 times. Your eye can see objects around 1 millimeter in size, so with 1000 times magnification you would be able to see objects 1000 times smaller - that is 1 micrometer. 1 micrometer is about the size of a bacteria, and about 10 times less than the thickness of aluminum foil. At that scale, if you looked at a strand of your hair, it would look very thick and you would see lots of small details.
There are more advanced microscopes that scientists use to look at much smaller things, especially if they are frozen in place. These microscopes look at how electrons (tiny particles smaller than atoms) bounce off an object, which a computer can use to make a picture of that object. The best of these "electron microscopes" can see individual atoms and how they are connected to each other.