Start with a well-stocked pantry
You need to have an arsenal of staple ingredients to start with because you're not going to be starting from scratch every time you go to the grocery store. Non-perishables in the pantry are stock items that you should always have on hand. There are also stock ingredients I always want available in the fridge and freezer.
I don't have a dedicated pantry stock-up day. Instead, as I run low on certain ingredients, I jot them down on my phone and do my best to buy them at my next grocery run (or wait for a sale if I know it's coming).
Here are the staple ingredients I always have on hand:
rice (short grain, long grain, jasmine, basmati)
pasta (long and short cut)
canned beans (black, red, cannellini, garbanzo)
canned tomato sauce (small 8 oz. cans)
canned tomato paste
spices and seasonings (salt, black pepper, cumin, chili powder, cayenne pepper, cinnamon, nutmeg, coriander, cardamom, turmeric, mustard powder, crushed pepper flakes)
dried herbs (basil, thyme, oregano, rosemary, bay leaves)
oil (olive, canola, coconut)
nuts (almonds, cashews, hazelnuts)
sugar (white, brown, powdered, agave nectar, maple syrup, corn syrup)
frozen vegetables (peas, corn, chopped spinach)
frozen fruit (mango, peach, berries)
thai chili peppers
Work with your budget and then plan meals
This one's an obvious one, but buying in bulk is more economical. If you have a membership to a warehouse store (e.g. Costco) then you can really benefit from bulk savings. If you don't, you can still buy in bulk.
My grocery store has "value buys" which I tend to see mostly in the protein department. A package of ground beef may be $4.99 per pound for a 1.5 pound package and make one meal ($7.49 per meal) or $2.99 per pound for a 4 pound package and make three meals ($11.96 total or $3.97 per meal). So, I tend to buy the bigger pack and portion it out and freeze what I know I won't be able to use up during the week.
Buying in bulk isn't limited to value packs. If the store is having an awesome sale on non-perishables, stocking up while the price is low also qualifies as bulk buying. I tend to reserve this type of hoarding for my favorite pantry items.
Extend the shelf life of your perishables
Use the fridge the way it was meant to and keep meats in the meat drawer, produce in the crisper drawers, butter and cheese in the little lidded compartment, etc. Temperature control is the main component of keeping food fresh.
Fresh herbs can be kept in vases of water in the fridge (like florists do with flowers) and they'll survive for weeks instead of days.
I also keep avocados in the fridge to prevent them from ripening too quickly. If I buy a bag of 5 avocados (bulk buying!), I'll leave one or two on the countertop to ripen while the rest are chucked in the fridge and taken out as needed.
Butter can be kept in the freezer and it'll keep for months, which is great if you've stocked up during a butter sale. Same goes for sesame seeds, nuts, and other foods with volatile oils.
If you've bought a bunch of protein in bulk and will not be consuming them within the week, wrap up the extras in cling film, aluminum foil, and then into a zip top baggie (labeled with contents and date) and chuck it into the freezer for future consumption. The multiple packing layers help prevent freezer burn.
Keep onions and garlic in a cool, dark, and well-ventilated spot (I keep them in little burlap bins in a drawer in the pantry).
Have a large bowl for produce that does not need to be refrigerated. I always leave my tomatoes at room temperature (refrigerating them makes them mealy) and pile fruit into a bowl on the counter.
Plan meals by theme
burgers one night and then to make the seasoned beef for bibimbap. Or fresh tomatoes can be used in pasta one night and then to make pico de gallo for a Mexican meal the next night.
After I have a theme and a general idea for a meal, I make sure to include a main protein, a vegetable dish, and a carb. Think about what you've got at home, that can also help round out each meal, whether it's frozen chicken in the freezer, a bag of potatoes in the pantry, or even fresh cucumbers from the garden.
And don't be afraid to take a little help from the store. Buy jarred tomato sauces, minute rice, pre-marinated meats; whatever shortcuts you want to take to make a home-cooked meal are great, as long as you are cooking!
Build up a recipe repertoire
I got into cooking by watching tons of Food Network as a kid. I picked up lots of tips (e.g. smashing garlic to get the skins off, rolling herbs for an easy chiffonade, undermixing the batter for tender pancakes) and it helped me to better understand flavor combinations and balance. My mom was the type to tell me to "get out of her kitchen" so I was rarely allowed to help (besides tasks like setting the table or washing dishes). So, I had to cook things on my own time, which was actually better because I got to experiment and do what I wanted to do. It's mainly about getting in the kitchen and getting your hands dirty. Practice makes perfect.
I also follow a bunch of food blogs (My Blue & White Kitchen, Smitten Kitchen, and What Katie Ate are three of my favorites) and glean a lot of inspiration there for recipes and I learn new cooking techniques and discover wholly new dishes that I've never heard of before.
And of course, I have good old fashioned cookbooks which make great resources and are enjoyable to read.
Make a list
When I'm at the grocery store, I tend to head to the protein section first to scout what's on sale. Then, I try and grab a variety - a cut of chicken, a cut of beef, a cut of pork, and fish - and then I head to the produce section and build up the meals from there. So, if I want to make chicken wings, I'll also grab bell peppers and tomatoes to make a pizza to eat with the wings. If I want to make a steak, I'll grab some frisee, haricots verts, and mushrooms to make a salad and sides to go alongside it.
Plan daily meals
A lot of these tips are pretty specific to my lifestyle but I hope there were some tips in here that were helpful anyway.