Farming Quickstart/Recovery guide:
Make a small field - fields that are too large slow down farming a lot. 3x3 or 4x4 is just fine. Set that to plump helmets all year round.
Follow NecroRebel's guide for setting labors. Use 1 full-time farmer and 1 part-time farmer if your fort is <15 dwarves, use 2 full-time farmers if >15 dwarves.
After a year or so, whenever your farmer has stabilized the food situation, add another field. Have it grow 2 different things. Also, add another farmer.
Keep adding fields/farmers whenever they seem to be needed until you get to 5 4x4 fields (80 tiles total). You shouldn't need to go above that.
Explanations and Detailed Info:
In the latest version you don't need to flood soil. Farms can be made in regular soil. Stone still needs to be flooded.
Too many fields will overwhelm your farmers, so if you have few farmers/low-skill farmers you should only use a few fields. You really don't need that much space planted to feed your fort.
Farming works by:
1) Assigning a dedicated farmer, possibly 2.
2) Building a farm plot in soil or on flooded stone (the soil can be under or above ground).
3) Picking the seeds to be planted. A couple of tricks here:
a. You want to have the same plant in a field for 2+ seasons. Why? When the season changes, plants that aren't harvest and are of a different type than is assigned to a field for the new season disappear. Example: Pig tail is assigned to a field for Season A. Dimple cups are assigned for Season B. When Seasons switch from A to B, all the unharvested pig tail plants will disappear. If both Seasons A and B are pig tails, the unharvested plants will not disappear.
b. Some plants are edible raw. Some plants are edible after processing. Some plants can be brewed, and some cannot. Some are only good for the cloth industry. The wiki is pretty clear on which one is which. #1 plant is plump helmets, good for cooking, eating raw and brewing.
c. Plants only give up seeds after processing - eating, brewing or processing in a farmer's workshop. You may have more seeds than you think, and more food than you think. Cooking does not return seeds.
Brewing:
Labors are probably the biggest obstacle here too. Make sure you have a full-time brewer, and possibly a part-time brewer also. The other big obstacle is having enough plants - a more structured farm will help with that.
Keep in mind that the first year or two is not the time to embark on grand adventures. The priorities are food, drink, bedrooms and trading material so you can get the other things you need in Autumn.
We've all been new, don't worry about asking questions. We're happy to help!