I just pour the grease from mine into a ramekin and then put that in the refrigerator, optionally cover it with plastic wrap if you are worried about contamination or smell. Most people use a jar with a lid but I don't cook fatty meats often enough to need a jar for all the grease I produce. If you left the pan out after cooking/overnight and the grease solidified before you could pour it, just heat it up again on the stove or in the oven until it turns back into a liquid. Obviously, wait until the pan has cooled enough to handle it without burning yourself while doing this pouring step, hot grease burns like hell and will send you straight to the emergency room with 3rd degree burns if it gets spilled on you.

Once it's in the container and in the refrigerator, it will solidify into a scoopable/spreadable semi-solid with a texture somewhere in between butter and ice cream. You can use it in place of fats or oils in other recipes (for example, if you need to grease a pan with butter or cooking spray before cooking, you can use a spoonful of the solid bacon grease instead). If you don't want to use it and just want to dispose of it safely instead, just wait for it to solidify in the fridge and then scoop it into the trash. Takes about two seconds and won't clog your plumbing

It does go bad eventually. The grease will get rancid if left alone for too long, and it will start to smell foul and anything you cook with it will taste terrible and make you sick. If you are going to save it, use it within a month or so if you leave it uncovered, or covered it can last longer but give it a smell test before you put it in a pan - it should have a neutral smell at room temperature and be white in color or have a very slight yellowish hue. Throw it out if you see any spots or discoloration.

A steak cooked in bacon grease is next level delicious. You should try it.