Your primary concern may be not starving to death, but you also have to keep an eye on temperature, sanity, and overall health. Many items in the game will help you keep these levels optimal. Once you gather enough materials, the game will give you a sound and visual notification to the left of the screen where your crafting is done. Many things are locked and the first thing to do with them is "prototype," which is essentially craft. In order to craft more advanced things in the game, you're going to need to build a Science Machine, but that's only where it begins.
There are many tools in the game that will help you survive and are pretty intuitive such as torches, camp fires, axes, shovels, pickaxes, and more. However, your character has a limited number of inventory slots, so you will have to manage what you carry around. You can expand on this by crafting a backpack, but you cannot wear armor and the backpack at the same time. You can also only hold one thing at a time, for instance you cannot hold a torch and a pickaxe at the same time.
There are many creatures in the game. Some are docile, some are hostile. Beefalos are one of the game's most popular creatures. It is often wise to begin to build a base near them for a good supply of manure, which is needed for farming. They can also be used as defense against hostile creatures. For instance, after about a couple of weeks of survival, you will be attacked by hounds. If you get them to chase you near Beefalo, they can "aggro" the Beefalo and you'll be defended. Other creatures include tentacles, spiders, bats, birds, bees, moles, and many more.
You gain experience points by surviving. However, these points are not used to level up your character's stats, instead they are used to unlock other playable characters. There are a nice variety of these, each with their own "quirks." For instance, the beginning character can grow a beard, which will help him keep warm. Another character is immune to fire and will light things on fire if her sanity drops. Another character can summon her dead sister, who really helps out with combat. Almost all of the available characters can be unlocked this way, except for a few. One of which requires the player to complete Adventure Mode.
I personally haven't experienced Adventure Mode very much, but I know that it is a place you can go that contains much of the game's challenges. These can be difficult and it is important to be prepared for them.
Don't Starve is a single-player game, however there is a multiplayer version called Don't Starve Together. I bought a pack, when I bought the game months ago, that included both games, the Reign of Giants DLC, and an extra code for Don't Starve Together. If you want the code, feel free to send me a private message and I'll see if I can figure out how to give it to you.
The game can be challenging, but fun as well. I recommend it. Below, I will include some videos that I've been watching. After playing for a few hours, I thought it would be good to watch how someone else played the game so that I might be able to survive longer. I found this task difficult as there weren't many up-to-date videos on YouTube and some people didn't know what they were doing either. I did, however, stumble upon a great playlist which I'll share below.
I should also mention that some people who have bought the game have received an extra game code to give to a friend. So, if you know someone who owns the game and you're interested, ask them if they have an extra code, maybe they'll share.
So far, I've survived a maximum of probably 16 days on one play through. That's not even a whole season. Yes, the DLC includes seasons and other additions, which can be toggled on or off when you create a new game.
Paul Soares, Jr.'s Don't Starve Indie Game Test Drive video: http://youtu.be/pUJSGoVzq34
A good Don't Starve guide playlist: http://youtu.be/uc_y4VdldLs?list=PLAk5nLibEkcfqnuKzQfPlPf9BcpFCffGO
Don't Starve on Steam: http://store.steampowered.com/app/219740/