I use more "modern" field agriculture, which means I remove all trees in the farming area and prepare the soil in square tiles. This part of the clearing is performed during the first winter (I start my characters in "spring"). This part also contains preparing for the burning by cutting and placing branches so they're ready to be set on fire.
My plots are 9*9, and I place branches on every second row, so I set fire at one row, and by the time I've set fire to the last tile the first one has burned out, so I can then go back to prepare the soil there. Depending on the RNG, I can generally prepare 2-3 rows per day (preparation includes having food for the two months it takes to prepare all of my rather extensive farming area). Once I've prepared the soil in the pre prepared tiles, I place branches on the rows in between (using stacks of branches prepared in advance) and then do a second pass to take care of those.
If you don't remove trees the fires can set trees on fire, which may potentially connect lines of branches so that more is burned than you had intended. It's worth noting that lighting a fire in a tile adjacent to a tile on fire is a lot easier than to set fire on an isolated tile (I think it never fails), which is a reason to go for lines or rectangles of branches.
I plant seeds as soon as I can, so the seed selection for plots depends on the order in which they're prepared. Check the wiki on to see which seeds can be planted in which months. Turnips are good beginners crops as they are large and give a good yield even with a poor skill. In addition to that, you can get two crops per year out of them if the frost isn't late in departing. Also note that different crops wither at different times (again, check the wiki).
Also note that you need a mod to make clothing out of your agriculture, as the vanilla game only provides food.
There are basically three kinds of crops: cereal (rye and barley), veggies (turnips, peas, broad beans [I may have missed something]), and spices, plus seeds. What you can make depends on whether you use vanilla or a mod (I use the Njerp Cooking Mod).
I start with turnips, rye/barley (barley is actually more nutritious, but has lower yield), and hemp and/or nettles, and gradually replace turnips with broad beans (peas are inferior to broad beans for everything), and change to yarrow for spicing eventually (it's a fair bit of work to collect the seeds, and a bit messy to grow them as you have to forego flowers to get seeds, and the yield is fairly poor as they're small).