Your car's brakes are obviously very important for controlling the car and keeping you safe on the road, which is why you don't want to overlook any problems you might be having with them. Ignoring a problem with the brakes often simply means that it will get worse over time, and the brakes may outright fail when on the road. While some brake repairs might be within your scope of expertise, others are best left to a repair shop, so note a few common problems with car's brakes so you know where to start looking and what to expect by way of repairs.
If you release the brake pedal, but the brakes still grip the tires, this is probably a problem with the calipers. The calipers are small clips that push the brake pads against the tires; when the calipers fail, they may not release the pads quickly when you let off the brake pedal. You can test the calipers by taking apart the braking system and having someone press and then release the brake pedal; if the calipers are slow to open, they need replacing.
If your car's brakes work fine but then seem soft and don't grip, and this intermittent cycle continues, the brake lines may need to be bled. The brakes work with fluid that builds up pressure and allows the calipers to grip or push the pads closed, as mentioned above. When there is air in the brake lines, this fluid cannot always build up the power it needs to operate the brakes properly. As the air in the lines makes its way to the brake pads and then back again, you will have intermittent power with the brakes. Bleeding the lines typically means draining the fluid completely so you get all air out and then refilling the lines while pumping the brake pedal, which forces out any leftover air.
If brakes grind, the pads are probably worn down and they are grinding against the rotors. In some cases, pads may slip out of place and then grind against the rotors since they're not gripping them evenly. This often means they need replacing. If the brakes squeal, this can also mean the pads are worn and you're metal against metal. If you notice these sounds just in the morning or after inclement weather, the pads may simply be wet and need to dry out and may not need replacing at all.