Note: I know there are quite a lot of other guides, but I thought I'd give it a go and try to explain this myself as well. I'll try to write this as for myself when I was still new. So, let's start...
Terraria is a game about building, exploring and fighting, but it is more than that. Here you can do pretty much anything you want. You'll need to try it out yourself to realize why it's so much fun!
The first time you'll start up Terraria, you'll be greeted by the main menu, see the picure to the right. You'll likely want to start out in Single Player, so choose it. Or, if you want to play with friends, choose Multiplayer (I don't recommend playing with strangers at first because most people will be more advanced than you). I'll assume you choose Single Player.
Now you'll see a list of all your characters (it's empty for now). You'll need to make
a character before you can play. Just click on "Create Character" and you'll see this:
Change your hairstyle, clothes etc. until you like how you look. Then, click the "Create" button. Give it a name, and the list of characters will appear again, so choose the one you just made. You'll need to make a world now. Click on "Create World", and choose a world size. You'll need to wait some time, depending on how powerful your computer is, but eventually it will finish and all you'll need to do will be to click on your new world and get ready for Terraria!
In the picture to the right you can see me, just arrived in the world of Terraria. You'll notice a few things:
My inventory: It's that bar in the top right. You can see that I already have a copper pickaxe, a copper axe and a copper shortsword. I'm gonna talk about these in a minute.
My health: Yes, that's what the hearts are for. For now, I have 100 life, but you can get more by using heart crystals.
The Guide: That guy running away to the right of the screen. He's here to help you out. Well, I'm here for the exact same purpose so...
Trees: These are important.
Why are trees important? You guessed it, you can build houses and craft tools out of wood. Sure, you can't use trees... you'll need to cut them down. Click on your copper axe, and then go to a tree and simply click on it and
hold. It's gonna take a while because your axe is very weak, but later on it will be much faster.Here you can see me cutting down a tree. Notice how I cleaned up a nice smooth area? I'm gonna build my house there, using the wood from the trees I just cut.But first, more on the inventory. It's critical to your (efficient) survival in these lands.You can see that it has ten slots... or has it? (hint: no, it doesn't). Press the Esc button, and your full 40-slot inventory will appear. It's quite empty and well organized right now, but unfortunately it's not gonna stay like this too long.Moving things around is easy. Just click on an item to pick it up, and click on another slot to put it there. If only tidying it up would be as easy... well, it is, but for some reason I simply can't do it. For now, just put the wood in the top row so you can use it, and close your inventory by pressing Esc again.
Click on the wood in your hotbar (that's how we call the first row of items) and use it to start building your house. Placing blocks is easy too, all you need to do is to click in the world with a kind of block selected. Make sure you start from the floor: even in video games, building houses starts with the floor and not with the roof.
If you want to remove a block of wood you placed, use your axe on it.
Now that you're safe inside, you'll want to start crafting. In your inventory, assuming you've got enough wood, you'll see crafting options to the left. Make a workbench, simply click on it, and place it inside your house like you did with the wood blocks. You'll notice that, if you're standing next to a workbench, you've got a lot more crafting options than before. Make some wooden walls, and place them so that your house doesn't have holes anymore. Also, if you have enough wood
remaining, you should make doors. These open and close so you can go out easily, but monsters can't.
Now that you have a nice house, you'll probably want to go out and explore. Be on the lookout for ores and precious metals: for example, I found some copper. This will likely be the first mining you'll do. Again, it's easy! Just use your pickaxe on tiles just like you used your axe on trees. There's not too much else to it. Just explore your world and collect ores if you see them. If you see slimes, you should kill them. They look like balls of goo and jump. But be careful, they can attack you too. You might need to build to continue your expedition. Oh, and make sure that you come home before nightfall.
Now it's night. You're (hopefully!) safe inside your house. One thing you'll notice is that it's very dark. You should make some torches. You guessed it, the crafting menu in your inventory. For torches you'll need gel fromthe slimes and wood. Hopefully you've got both, otherwise it's gonna be a long, dark night. Another thing you'll notice is that you'll be attacked by zombies and flying eyes. You can attack them, but it's probably best for you to stay home for now. They're not smart enough to break doors or walls, so as long as you're inside you'll be fine.
Your next target should be to get someone to live in your town. They'll need a decent home to live in. By "decent" I mean that it should have at least a chair, a table and a light source. It also needs walls.
Well, this is pretty much it. Find caves, explore, dig, mine, make better weapons and tools and eventually you'll be able to take on the strongest of monsters and become the ruler of your lands. Until you play Multiplayer, that is.
This guide took me more than an hour to write and I had to add a lot of images to the "newest images" section. But I hope it will be worth it. Hope this helps!