Bought a new will remote but it doesn't work.
Check the battery levels. You can do this by pressing A. If all 4 lights flash on and off, your batteries are completely charged. 3 lights, 2 lights, and 1 light signify 3/4, 1/2, and 1/4 battery levels. If lights don't flash, replace/insert batteries.
If it's not working with your console, open up the battery cover and the flip lid on the front of the console. (If it's a Wii U, you don't need to open the flip lid.) In both places, there is a red button. (On Wii U, it's next to the flip lid.) Press both red buttons at the same time. (Your Wii will need to be powered on.) The Wii Remote will continuously flash lights until it either receives a sync signal or about a minute has passed; whichever comes first. If you've pressed the buttons and your remote is still flashing, press the button on the console again. Once the remote is synced, the flashing lights will turn into a single light; the placement of the light will vary depending on how many remotes are signed into the Wii.
*Note* Once your remote is synced, you simply need to press A to sign back in if your remote turns off.
If all of the above steps were followed, and your remote is still not functioning, contact the manufacturer. Brands such as Nintendo and Nyko are usually okay, but generics like GameStop aren't the best. It's often easiest to return it and buy a different brand.