I am a beginner in gardening, so I appreciate some tips on how to grow mint plants.
Stormy has a nice answer, but I should add a WARNING: mint can be invasive on your garden, so don't plant in the middle of your garden and keep in mind: How do I eradicate Mint .
Is this mint out of doors in your garden? Mint is a good plant to learn with. Doubt you'll be able to kill it. It is one of the hardiest and can easily become a weed. I am thinking you had a hard freeze and then the sun came up to thaw the frozen leaves too quickly. Totally normal. Leave your plant alone for the winter. The leaves that freeze and die will help the rest of the plant survive by adding more air pockets, decomposing organic material that puts off heat and hopefully your mint is getting covered by snow. One of the best protectants of plants in the cold. In the spring get your hedging shears (two handed chop chop, bypass, used to cut hedges properly) and chop down the dead plant material to allow the new leaves to emerge. (Use alcohol to clean your blades between each and every plant). Rake up the debris and spread on your compost pile. Trees should be pruned to thin versus deadheading. Deciduous plants get rid of their leaves before the leaves can freeze. In the fall I leave all this material on my beds, the dead leaves, etc. In the spring, I clean up the fibrous stuff and put it in the compost. Twigs, branches are in a separate pile altogether as they take a long time to decompose. I get a chipper once per year to speed up the decomposition.
Is this mint in a pot or in the soil of your garden? That makes a huge difference. If your mint is in the garden soil it should come back in the spring just fine. Try to consider ways to control the spread of your mint. Taking the flowers/seeds off is critical before they become viable (use that good ole chop chop two handed shears), do you know how to sharpen? if you go out to buy a pair go with Sandovar (I think that is the name, used to be Felco?) Felco is great for all hand pruning tools. Corona is marginal. But better than cheapie no name tools. You want to buy a tool only once.
Send a picture and more information. This is the best I can do shooting in the dark. Oh, you could head back your mint part way and dehydrate the leaves for culinary uses. Then take your plants down further in the spring. Good luck trying to kill mint!! Have you tried Chocolate mint???