Most geraniums are considered an annual in areas with winters. I went ahead and assumed your geranium is a Martha Washington because of the few flowers I can see drooping over the edge. I've never saved geraniums but I've heard others saving their roots, which hopefully are still viable in your pot because the rest is toast.
I am posting a site that tells you how to 'over winter' your geranium. Do not expect greenery and flowers this winter. It looks like your geranium froze while out of doors?
You need to cut off all of the dead top growth and keep it cool, not frozen. A garage might be a better place to over winter this plant. Forget light, do not water regularly as this plant is in dormancy. Forget fertilizer as well! You want to keep the roots from freezing and from rot.
Some people actually dig the roots up and store just the roots as this article explains. What soil is in this pot? Is this the original soil and pot from a nursery? If this soil is garden soil you should dig the roots up to store. If in potting medium leave them in the pot.
Let us know if this information makes sense and works for you. Otherwise, throwing the plant out in your 'compost pile' and starting over in the spring with a new fresh geranium is what I would do. When replanting in the spring only use sterilized potting soil without moisture holding gimmicks and added fertilizer. You want to add fertilizer separately and use half of what the directions say. A balanced fertilizer with NPK, not blood meal, nor fish fertilizer. Equal numbers or keep N the lowest of the 3 percentages to promote flowering. Osmocote 14-14-14 all purpose works very well! Half of what is directed. You will probably only do one application in the spring for the entire season. I would transplant into fresh potting soil in the spring and then add the fertilizer.
The best place for a geranium is on a covered porch, no direct sunlight. If you want this plant in direct sunlight, get it transplanted and allow it to grow IN the sunlight. Acclimation to direct sunlight or differing lighting is very important. You can't just take an indoor grown plant and put it out of doors in the sun. Usually means death. Nor can you take a plant used to the out of doors and sunlight back into the indoors even with the direct sunlight from a south facing window without acclimation.
Plants in pots have roots that are susceptible to too high temperatures and too low temperatures. I am hoping that this plant wasn't out side long enough to have frozen roots or none of this will work.
overwintering Martha Washington Geraniums
NOTE: Is your garage a detached garage? Newspaper is incredible insulation. I would lightly water the soil and wrap the entire pot and plant in newspapers. Use masking tape to secure the paper to itself. Keep it loose and airy. Leave a few gaps for air, crunch it up somewhat to allow gaps between layers. Do at least 5 layers. Make sure the pot is very well covered including the bottom. It will look like an ugly ball of newspaper. If there is a wall shared with the home keep it snuggled up to that wall. That should work fine for the entire winter. When it warms up in the spring, put it where you want it to stay and water well. When your plant has grown leaves, I would then replace the coco fiber matt, cut off any browned or mushy roots, use fresh potting soil and transplant gently. Now would be a good time to add Osmocote Extended Release fertilizer. This fertilizer lasts 4 to 6 months so you won't need to add anymore for the season, before you repeat winterizing. Take a picture of the root ball in the spring and send it to us? Certainly, let us know if this worked for you. The next year, you might have to root prune harder to continue using this pot. Fresh coco liner every year, raw burlap fabric works well as a substitute for the liner, cheaper, too. If this works, you might think about a second pot, hopefully the same brand/style with a bowl shape? Cut the root ball in two or three chunks for 2 and 3 more plants? Power in mass plantings of the same plant! Watch for insects. Don't over water. Water completely when you water and simply check the heft by lifting the pot slightly with your hand as it hangs. If heavy don't water, you'll be able to tell if it is light and thus needing watered. Heavy waterings when you water. Don't water again until you feel the lightness of the pot/soil/plant by pushing up on the bottom of the pot. Try to keep the plant height at least eye level and below. There are pot hanger extenders so you can make an interesting hanging pot grouping. Pinch off flowers as soon as you can stomach doing so...the more flowers you take off the harder your plant will work at making more and more flowers. Keep debris off the top of the soil. You could also add other plants with the geraniums as well as in their own pots for this hanging pot composition. Don't get carried away. I would add just one other type of plant; Orange sedge or Carex testacea. A bright green lovely ornamental grass, very fine in texture with 'glints' of orange that won't clash with the pinks/purple at all. Trim those by gathering the entire wad of grass, twist and simply cut the end bit straight across and release. Next spring look for this plant and plant it in its own pot that matches this pot, very pretty pot! Classy. Same style or at least black wire with coco liner. I would also refresh my geraniums from time to time with new ones. I'll go check the name.