Check out my article on growing sprouts - truly the simplest way to grow food indoors in winter.
Growing seeds in soil indoors in winter is a bit more complicated. You can try in a sunny south facing window, but your success will depend on how much sunlight you get.
I am located in a little valley and the hours of sunshine are very limited in winter. For me to grow food indoors, I need grow lights. That said, they are not particularly expensive nor is my set up elaborate. It is of moderate quality but it has lasted well over a decade with no real sign of deterioration. I haven't even needed to replace the fluorescent bulbs.
You will need both lights and a way to raise and lower them. My set up offers a metal frame with trays and light fixtures suspended by chains.
You want to choose bulbs between 4000 and 6000 kelvin to help mimic outdoor or greenhouse growth. When seeds first come up, you will want to place your lights within 4 inches of your plants. Once they are established ( have a second set of seeds) you can raise them a bit. Plants that need more light grow searching for it by getting too tall and 'spindly." Give them 12 to 18 hours of light per day. A timer is your best bet as they need a dark period as well.
Plant your seeds in pots of dampened (not wet) organic potting soil at the depth recommended by your seed packets. Make sure they have at least 4 - 3/8" drain holes. You can reuse plastic container if you make sure they have adequate drainage.
Remember: Plants don't like cold feet. They don't like wet feet.
Properly moist soil will feel a bit cool and, well, moist. Dry soil will be granular and not stick together. If in doubt, begin to pay attention. After watering, notice how the soil feels. Notice again in one day. In general it is better to under water than over water until you have some confidence.
Wilty plants need water. Check them daily. When you water, consider using room temperature water. You can fill your watering can and let it sit overnight, for example. Or simply add a little hot water to the watering can.
I have successfully grown basil, spinach and lettuce greens indoors. You probably won't get heads of lettuce, but you can get some great small greens to enjoy with your sprouts on a sandwich or even a salad. Last winter, I grew enough basil to make a wonderful fresh pesto.
Another fun type of edible you can grow are the herbs you will find in the grocery store. I have several rosemary growing which I harvest throughout the winter for making rosemary shortbread. I also grow sage I brought in from the garden and enjoy it in salad dressings or crumbled over roast chicken.
Mint and basil are commonly found in the grocery store. They will greatly appreciate a bigger pot when you get them home. And then to get under the grow lights, if you have them. You can trim them here and there to add to your recipes.
Whatever you decide to try, you will learn and likely enjoy the pleasure of growing your own food indoors in winter.