There are mainly three types of galaxies:
elliptical, spiral, and irregular.
Elliptical galaxies can look anywhere between elongated to spherical. There is not much structure to these galaxies, nor is there much gas or radiation between systems in these galaxies.

Spiral galaxies look like pinwheels, with spiraling arms coming from the center, and most of the stars and visible matter are concentrated on one plane (think disk-shaped).

Irregular galaxies are those that cannot be called either spiral or elliptical.

There are also a few other minor types that do not appear often, at least as far as we can see, such as ring galaxies.

Galaxies are divided into three main types based on what they look like: spiral galaxies with arms of stars and dust, elliptical galaxies that are sort of balls of stars orbiting each-other, and irregular galaxies that have been torn apart or are being disturbed from other galaxy types. Usually, elliptical galaxies are the oldest and reddest, while irregular galaxies are the youngest and bluest, but there are exceptions.