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Hearthfire DLC gives you the ability to build huge mansions, custom tailored to your needs, but this is not a free-form building system. Think of it, instead, as a single house plan with a few different options to choose. You first consult your plans, then you move to your house building bench and you determine a part to build, secure the required materials and then click to select that part and it's built immediately onto your house.
The materials required include: lumber and special smithing items, such as nails, iron fittings, hinges and locks. You can make the smithing items yourself, right next to the house building table, as long as you have the materials. It can be handy to build the outdoor smelter, so you can smelt down ore into ingots and then move to the anvil and make your building materials without having to do much traveling. The required lumber comes from a nearby lumber pile, which holds the lumber you have bought for building (including some lumber you get when you buy the home site). Don't worry about moving your lumber around, however, your lumber is available at all of your building sites. To get more lumber, you can either trek into a town and order some from the owner of the lumber mill, or you can hire a steward for your home and have them take care of buying the lumber. If you hire your companion as steward of your home, you can have them join you on your adventures again by talking to them and scrolling to the bottom of the discussion list.
When building your home, you create a small home, first. You can leave it at that, if you like, or you can continue your building and create a much larger room behind the small home and then convert the small part into an entry into the large house.
From there, you can add three additions (on the remaining three sides other than entry room. Each of these three sides can be one of three different types of structures: a flat-topped addition, a slanted-roof addition or a tower. You can choose the type individually for each side, allowing you to have one of each, or a home with three towers around the outside, if you like. The choices for each side, however, are only allowed on that side, so if for example, you want to have an Alchemy table in your house, you would need to have the Alchemy Tower, which is only an option for one wing of the house. This also means that you may have to make some tough decisions, since you might find that you're interested in more than one option that are both only available on a given wing.
