This achievement is very easy:
Chop wood
When you enter Riverwood from the southwest gate, there will be a sawmill on your left. Walk passed behind it and turn to the right. After the hulk on your left you should find a table riverside with a lumberjack axe on it; pick it up. Behind the little fence in front of you (just behind the grindstone), there is a block of wood and some logs. Cut the logs with your axe. Chopped wood can be sold for gold.
Mine ore
You can go to Embershard Mine for this one. Once you got rid of a few bandits, look at the end of the camp down by the right of the bridge by which you came around and you should find a pickaxe. Now go to the end of the mine and you should find an iron ore vein. Use your pickaxe on it and bingo! As a general rule, you should find an exploitable mine by any site indicated with an hammer and pick symbol on the map.
Cook food
When you are about to enter Riverwood from the southwest gate, there will be a fire with some cooking pots hanged on a wooden structure. Provided you have the required ingredients (vegetables, meat, potatoes, fish, salt...) you will be able to cook something there. The game actually tells you what ingredients you require for brewing a course, so if you miss anything you know what to find. Anyway, a simple recipe is salt with whatever animal flesh.
Once you completed each of these three actions at least once, earn this achievement.