First of all, you absolutely need protection to look at the Sun, there is no way around this. Serious, irreparable, life altering damage can occur if you do not follow proper safety precautions. If you do follow the relatively simple safety precautions, observing the Sun can be a very rewarding and insightful experience.
If you want to know why these precautions are important, click on the link below. Note, please don't try this at home.
If you want to observe the Sun safely and meaningfully, keep reading on!
The sun, making up 99.8% of all of the mass in our solar system, is a notable object for learning about astronomy. Its cyclical activity governor's many characteristics of our solar system, and is something that is relatively easy for amateur observers to track.
The sun's activity falls into ~11 year cycles, which stem from the changing of the magnetic field of the sun. At solar maximum, the poles of the sun switch before activity declines again to solar minimum.
The solar cycle is most notably marked by the appearance of sunspots, dark spots on the surface of the sun that signal activity in that area, and are a means by which the magnetic field changes. As the cycle begins to grow from solar minimum, where there may be none present for an extended period of time, sunspots will begin to appear near the poles of the sun, working down towards the equator as activity grows stronger. Several sunspots are visible in the image on the left, which was taken with a Celestron 130GT here on campus.
Given the ease of viewing them, (semi-)consistent viewing and documenting of sunspots is a great way to track an astronomical process on your own.
The composite image shown here contrasts the suns activity at solar minimum (shown on the right) with the sun's activity at solar maximum (left). (NASA/IDO, 2014)
Want to know what to look for, or see what you're looking at across some different light spectrums that give you more information about what's happening on the Sun's surface? NASA keeps a database online of "live" photos of the Sun, ranging from white-light (the way we see it, too) to magnetographs, which show the magnetic nature of sunspots. (NASA/SDO, AIA, EVE, and HMI science teams)
Solar Cycle 25: https://www.nasa.gov/press-release/solar-cycle-25-is-here-nasa-noaa-scientists-explain-what-that-means
SDO Live Sun Database: https://sdo.gsfc.nasa.gov/data/
NASA Solar System, the Sun: https://solarsystem.nasa.gov/solar-system/sun/overview/
Tracking Sunspots Video from NASA: https://youtu.be/rx9m6H6GeLs