Sorting out your beds
Starting out you can't do much until you figure out the sort of beds you will be growing in, which means you need to look at your property and what you have to work with. You need to know the ph of your soil, which you can find testing kits at your local gardening or farm supply store, this can also come as your local hardware store. A good ph level for a vegetable garden is usually between 6.5 - 7.0, if you've got this, your golden. If not, then your soil may need amending. If it's low, then it's rather acidic and the number of things that will grow is sparce, so adding eggshells, wood ash, or lime will help. Keep in mind the more an additive has to break down, the slower your ph will increase.
If your ph is high then it's lacking the proper nutrients that most plants need to thrive, and adding things such a compost or manure will help immensely. If you live in an area where there are farms many farmers will sell their manure in large quantities and at a better value. The cost will depend on the farmer, and if they have to deliver that might cost you extra so be sure to ask. If it will cost you to have it delivered, it might be best to arrange to collect the manure yourself if that's an option.
Now, your beds.
For some, tilling up a section of your yard and planting straight in the ground works very well, and presents very little issue for you. You amend your soil accordingly, checking to make sure you aren't overly amending, and can get planting. It's always fun to get down on your hands and knees and dig a hole in the earth and pop in those first seeds. You need to make sure that wherever you decide to put your garden its an area that gets plenty of sun, and can be easily watered. While some plants don't mind a little bit of shade most like large amounts of sunshine to thrive.
Also, look at the area once you've figured out the best place for your garden. Some plants, like peas, bean, and some tomato breed, need structure to support them. Is there a fence along the area that can act as a trellis that your can tie your plants to or climb upon; after all if it's already there, then it cost nothing. If you don't have a fence or anything for the plants to grow against, then you need to sort out what to do, and a section of old field fencing if you have some between two stakes works very well, or getting some wire and running it along the area where your plants will grow between stakes works too. An even cheaper solution is to take some branches that have maybe fallen off a nearby tree, shove them into the ground and allow them to support lighter plants like your peas or beans. Again, before spending too much money on anything elaborate, look around and see what you have available to you, that might be there for the taking.
There are others that can't do in ground beds because of physical disabilities, or let's face it, age. This is where container, above ground, or raised bed options come into play. The thing with these sorts of beds, is that they can be costly to build if that's the route you are going. With the cost of wood being more than what many can manage you need to look for other options. Old tubs and totes work well, just make sure they are clean before you fill them with soil, as certain contaminants can be very harmful to your plants. Visit your local thrift stores, you'd be shocked what you might find that would make amazing planters, even estate salvage, tag sales, and auctions are good places to find low-cost alternatives. Keep an eye out at any specialty stores too, sometimes a store will get in items that were damaged and can't sell at full price or return to the manufacturer so you can pick them up for next to nothing.
End of season sales are a good place to look for containers and things to grow plants in. Many stores mark down costs on seasonal items to move them out to make room for the next season coming in. Clearance shelves make good places to find items as well, anything that is plenty deep enough will work, if you have an old kiddie pool, that's an amazing place for alliums.
I will say this again though, and I can't say it enough, BEFORE you go shopping, so look at what you already have lying around. Even a five-gallon bucket, makes for a good place to plant tomatoes. I was fortunate enough that my husband works for a company that had a bunch of old totes for holding massive quantities of water and other chemicals. We gave them a good scrubbing, cut them in half and now we have several raised beds to grow in.
Your plants.
When starting your garden you have to consider your plants, and think about the best growing conditions for them. Plants like mint, and horseradish tend to be rather invasive and will spread year after year. Mint will especially start popping up in places you didn't want it, so these plants will do best in containers to keep them from spreading beyond the area you want them. My oldest daughter went to plant Sweet Mint in a garden bed, but dug it up and placed it in a hanging basket after I warned her of what could happen.
Plants like squash and pumpkins need room to stretch so they need a lot of space, they also use a huge amount of nutrients as well, so placement is key. If growing these plants make sure your space can accommodate just how long their vines can actually get, I've had pumpkins with vines that stretched up to ten feet or more.
Another thing to consider is if you can go vertical. If you don't have a lot of space, even plants like squash and cucumbers do very well growing up a trellis. Again, old wire fencing, lattice, or even netting draped over an old greenhouse frame, some left over tubing or pipe from a plumbing project, makes for great climbing structures for your vining plants. My husband built an arch for peas between two raised beds. I took some stakes and tied them at the top like a teepee and have cucumbers growing up them.
I hope I haven't overwhelmed you, or discouraged you in any way, with an information overload. When starting a garden there is a lot to think about, and there will be more that I will touch on soon. This will hopefully give you something to think about, so you can have a thriving, beautiful space to enjoy.