The first cube you will learn to solve is the 3x3. This is what most people do first, and, in my opinion, it is probably best to learn this one first as well. Can you solve it already? You can then proceed with the 2x2 or other cubes.

 

Step 1:                                                                                                                                                                                                                                                                                                                                                            When you are learning how to solve the cube, it is useful to start every solve with the same color. Personally, I always started with white, like a lot of people, and so that will be how I will explain it as well.  Every solve starts with  a cross, which looks like this:

Solving the cross might even be the hardest step of solving the Rubik's Cube.

Before you actually start learning though, you'll want to know and understand that a cube is built up of three different types of pieces: center pieces, edge pieces and corner pieces. The center pieces are in the center of every face, and they indicate the color that should be on that face, since they can't move and only have one color. There is a total of six center pieces. Then you have the  twelve edge pieces, which have two colors each. For example, in the picture above you can see the white-red and the white-blue edge. You can also see the white side of two other edges. And finally there are the eight corner pieces, which have three colors each. The corners, along with the edges, are the pieces you have to solve. The centers are already solves, since they can't move. As seen in the picture, the cross consists of only four edges. 

Now, there is a reason I said that the cross is arguably the hardest part of the cube: it is all intuitive. There are methods people have devised to make it easier to grasp, but these methods are often really slow. Although it is difficult to intuitively solve the cross, I believe you can do it after a little practise. Just try it! If it doesn't work out, you can always look up a method to do it.

 

Step 3:

Next, we will solve the remaining four corners of the white face. For this, we will need some notation, so we all know which move we are talking about. There are six sides on a cube. A Front, Back, Up, Down, Right, and Left side. To indicate which side we are moving, we simply write down the first letter of this face. However, when we turn a side counterclockwise, we add a ' to the letter. So R' would mean that you turn the Right side towards the front (from the perspective of the right side, this is a counterclockwise move). You will also encounter moves like U2. The two simply means you turn the side twice. In this case the direction doesn't matter, because after a total of 4 turns the cube will be back in its original position anyways.

We now need two algorithms to be able to solve the rest of the white side:

The righty algorithm: U R U' R' 

The lefty algorithm: U' L' U L

Be comfortable doing these algorithms and make sure you can execute them quickly before you move on.