Aren’t all problems with your Android or other devices annoying? A welcome problem doesn’t exist, unless the problem is welcome because it diverts attention from another, preexisting problem. And random problems? If problems were predictable, they would serve in office. Or maybe they already do?
Here are some typical problems and suggestions for a solution:

You have general trouble

For just about any problem or minor quirk, consider restarting the phone: Turn off the phone, and then turn it on again. This procedure will most likely fix a majority of the annoying and quirky problems you encounter when using an Android phone.
Some Android phones feature the Restart command on the Phone Options menu: Press and hold down the Power/Lock key to see this menu. If a Restart command is there, use it to restart the phone and (you hope) fix whatever has gone awry.
When restarting doesn’t work, consider turning off the phone and removing its battery. Wait about 15 seconds, and then return the battery to the phone and turn on the phone again.

The touchscreen doesn’t work!

The touchscreen, such as the one used on your phone, requires a human finger for proper interaction. The phone interprets complicated electromagnetic physics between the human finger and the phone to determine where the touchscreen is being touched.
You can use the touchscreen while wearing special touchscreen gloves. Yes, they actually make such things. But wearing regular gloves? Nope.
The touchscreen might also fail when the battery power is low or when the phone has been physically damaged.

The data connection needs to be checked

Sometimes the data connection drops but the phone connection stays active. Check the status bar. If you see bars, you have a phone signal. When you don’t see the 4G, 3G, 1X, or Wi-Fi icon, the phone has no data signal.
Occasionally, the data signal suddenly drops for a minute or two. Wait and it comes back around. If it doesn’t, the cellular data network might be down, or you may simply be in an area with lousy service. Consider changing your location.
For wireless connections, you have to ensure that Wi-Fi is set up properly and working. Setup usually involves pestering the person who configured the Wi-Fi signal or made it available, such as the cheerful person in the green apron who serves you coffee.

The screen is too dark!

Android phones feature a teensy light sensor on the front. The sensor is used to adjust the touchscreen’s brightness based on the amount of ambient light at your location. If the sensor is covered, the screen can get very, very dark.
Ensure that you aren't unintentionally blocking the light sensor. Avoid buying a case or screen protector that obscures the sensor.
The automatic brightness setting might also be vexing you.

The battery doesn’t charge!

Start from the source: Is the wall socket providing power? Is the cord plugged in? The cable may be damaged, so try another cable.
When charging from a USB port on a computer, ensure that the computer is turned on. Computers provide no USB power when they’re turned off.
Some phones charge from a special cord, not the USB cable. Check to confirm that your phone is able to take a charge from the USB cable.

The phone won’t do landscape mode!

Just because an app doesn’t enter landscape mode doesn’t mean that it can enter landscape mode. Not every app takes advantage of the phone’s capability to orient itself in landscape mode. On certain Android phones, the Home screen doesn’t “do landscape” unless it’s placed into a car mount or has a physical keyboard that works in landscape mode.
One app that definitely does landscape mode is the web browser.
Android phones have a setting you can check to confirm that landscape orientation is active. Check the quick actions drawer for the Auto-Rotate setting. That setting might also be found in the Settings app, on the Display screen.

The phone gets so hot that it turns itself off!

Yikes! An overheating phone can be a nasty problem. Judge how hot the phone is by seeing whether you can hold it in your hand: When the phone is too hot to hold, it’s too hot. If you’re using the phone to keep your coffee warm, the phone is too hot.
Turn off the phone. Take out the battery and let it cool.
If the overheating problem continues, have the phone looked at for potential repair. The battery might need to be replaced.