I'm not that good at gardening, but these are some of my notes on the way I've done things.
Generally, you initially have to replace the grass (sod) that's growing on your lawn with good soil. Either:
You also need compost.
Next, make a box for the wood to go in. You can use 2x6 pieces of wood or something to make a box. Put the box where the grass used to be.
An alternative to replacing your lawn and making a box is to buy a VegTrug, which is a trough to put dirt in with a plastic cover accessory. It lets you grow certain vegetables earlier in the year (like a tiny greenhouse) and requires less weeding.
To get the soil to put in place of the grass, it has to be good soil. The bags you can buy at grocery stores seem to be bad quality. I ordered a cubic yard of soil to be delievered to my house in a truck, from a place I found on Kijiji (Capital City Dump Trailer Services - (506) 343 6537 - who may still be in the Yellow Pages). It was $70 for a cubic yard, cheaper than the bags you buy in grocery stores. Scott's Nursery is another option to get dirt delivered to you by truck. (Note: 1 cubic yard weighs 1700 pounds, and is a lot of dirt.)
In Knowlesville, they made soil out of swales - manure, straw, and sticks. That wasn't practical for me because I don't have manure or straw. There are other recipes for good soil too, some involving peat moss, which I haven't tried.
When the dirt arrives, put it in place of the grass that was there, and mix compost into it with a shovel (can also till it, but I used a shovel). Over the years, keep adding compost to it, otherwise it will gradually deplete in volume and nutrients. Initially add lots of water to it too.
Optionally, in Fredericton, you can get your soil tested at the Department of Agriculture before you start a garden. This costs a fee but tells you which nutrients you're deficient in so which might let you figure out what, if anything, you need to add to the soil, or what things will grow better than others. (I'm not sure whether you should test the soil that was already in your lawn or the new soil you're about to grow vegetables in. Maybe both?)
In Fredericton, you can get wood chips delivered to you for free from Wildwood tree services. They're a waste product from the city's landscaping activities. You have to accept a huge pile of them. They're useful to put on top of your soil to keep in moisture and help prevent the soil from getting too dry when it isn't raining for a while.
Another good way to either start or expand a garden is to start potatoes with the following steps in the springtime:
I did this and later in the year I had potato plants! At the end of the season, the place where the potatoes were growing is now no longer a lawn and is ready to become a raised bed to grow other things the next year. (You should still add soil to it and enclose it with, for example, 2x6es.)
When To Plant: Start in the spring, but it's different for every plant. As early as March for some things, and leeks in particular have to be started inside in February (I've never succeeded in growing leeks). Most things start in April or May, after the risk of frost. If you plant too early, then have a cold night, the frost can wipe out all your baby plants. It often works better, if you can, to start seedlings in your house early and transplant them when it gets warmer, but I don't usually do that because I believe plants are happier outside and probably don't like being transplanted.
Seeds: Buy packs of seeds or get them for free from the library (if you do, it's courteous to save some seeds from the plants that grow and donate them back to the library at the end of the season). The instructions on the packs of seeds tell you when to plant them, how far apart to plant them and how deep to plant them.
What To Plant: My strategy has been to initially try planting a bunch of things and see what survives, then plant more of that next year. Things that have been easy for me to grow are kale, peas and green beans, probably because I'm not good at gardening and those things don't require good soil.
Weeding: You pretty much have to weed and this is the most labour-intensive part of gardening. It's more important to do early on when your seedlings can't survive if there's too much competition. I usually wait until a plant gets a bit big before weeding it to make sure it's actually a weed.
Harvesting: With Kale, and many other plants, pick the bottom leaves just as they're starting to die or change colour. This saves the plant energy from not having to give energy to those less important leaves and it can then use the energy to make its other, newer leaves grow bigger.