To refine GhostDwemer's response a bit.
New players will run into two problems with the default embark.
1) Everyone hauls - which prevents other things from happening as urgently as they need.
2) You run out of barrels/pots.
This is a bit overkill, but it's a good habit to establish until you are consistently getting your food up and running:
1) Disable hauling jobs for your miner. Find a soil layer and dig out a suitable underground space for food/farms. I usually start with one 9x9 room, designate a food stockpile for everything except seeds and have my other dwarves haul all the food in from the wagon. After the first 9x9 room is done, I dig out a 2nd connected 9x9 room, which will contain the farms. When done, I designate a number of 3x3 farms with a 3x3 food stockpile in the middle which only allows seeds. This shortens the effort for your farmer. I then dig a 3rd connected 3x3 room and build a still and a kitchen.
2) Once you start the digging above, decide whether to make wooden barrels or stone pots. If you have a lot of wood and your woodcutters won't die getting to it, take your woodcutter, disable hauling, and have him cut at least 50 trees. In the room with the kitchen, build a carpenters workshop. If you go with stone pots, you'll have your miner start on those after digging those rooms out. Build a craft workshop next to the kitchen instead.
3) While that's happening, I usually take 2 dwarves, disable hauling except for food hauling, and enable all of the farming skills. These are your farmers/brewers/cooks. That's all they do. If you want, designate a 20x20 area or so aboveground for plant gathering and they can do that while the miner does his business.
4) As soon as the farms can be built, undesignate the plant gathering, build the farms, and set 2-3 of them to grow plump helmets. These are your staple crop. They can be eaten raw, cooked, and brewed into booze, and they grow fast. Do not cook them however - as that destroys the seeds. Brewing and eating raw preserves the seeds - and you'll need them. Set each of the other farms to grow the other crop types. Skip dimple cups as they're only useful for dye. Set yourself 10 brew jobs and 10 prepare simple meal jobs at the still and kitchen.
5) If you are going for stone pots, get your miner mining stone. Once you have either wood or stone, start building large pots or barrels. Give another one of your dwarves either carpentry or stone crafting skill, take them off of hauling, and have them make 50 pots/barrels. Early on, what tends to happen is that the plants and seeds that you gather fill up all of your empty barrels, and with no barrels, you can't produce booze. So you typically need to get a healthy number of barrels produced early on.
6) Once you get enough space mined out/cleared, I build a 9x9 or so furniture stockpile which only accepts barrels/large pots, another which only accepts plants, another which only accepts booze, and a 3rd which only accepts prepared meals. The prepared meals stockpile is set with a maximum barrel of 0, so they won't be put in barrels (oftentimes there will only be one meal per barrel, which is a waste of barrels, and its easier to trade meals out of barrels). Make sure you dwarves aren't walking through that room any more than necessary or they'll get destroyed, but otherwise this is safe. These give you a good visual cue where your food industry is. If you are out of barrels, you won't be able to brew. If you are out of plants, you won't be able to brew. If you are out of booze, you're in trouble. If you're out of prepared meals, you might be in trouble. I usually also have a meat/fish stockpile and a milled plant/leaves stockpile. Dwarves will eat meat/fish without processing, so if there's barrels there, you're good even without prepared meals. Dwarves can't eat milled plant/leaves, and while these are good for prepared meals, if you have a fortress full of nothing but sugar, you'll starve.
I find it's good for new players to have very visible measures of where they are on food/booze. When everything is mixed up in the food stockpile, along with a bunch of empty barrels because there's no furniture stockpile for them to go to, then they never really know if they have usable food or not. Eventually, you'll develop a feel for where you are and be able to better use the overview screen to gauge things. Also, by segregating the farmers out from all other activities, it helps make sure that some giant stone hauling activity or such doesn't distract them from feeding the fortress.