So while I am trying to work on tips for people getting into cubing, I was reminded that I skipped some fundamental concepts. All of you people that are already under three minutes probably don't need to read this one, so you'll probably have to wait for me to type Part 3.
The standard 3x3x3 Rubik's cube has three distinct types of visible pieces. There are six center pieces of a single color, all of which are attached to the center spindle. These six pieces cannot move relative to each other. There are twelve edge pieces, each with two colors. There are eight corner pieces, with with three colors. Each of the pieces has a unique set of colors that correspond to the final location of the piece. For example, the green and white edge has a final location that is on the edge between the green and the white center pieces. The corner piece that is orange, green, and white corresponds to the location of corner of the three faces that have the orange, green, and white centers. Since the centers cannot move relative to each other, all that is really happening is that there are twenty pieces moving freely around the center pieces. This is a little bit different from what many people initially see - often the first impression of a Rubik's cube they have is that there are 54 stickers. (They're at least colored tiles now, anyway.)
The next part of conceptual understanding is the idea that any specific set of actions performed on the cube always has the same effect on the cube, and thereby can be used to perform predictable operations on the cube. These operations are usually referred to as algorithms.
We typically describe algorithms as a specific ordered set of face turns, described in relative terms. Instead of using the colors of the faces, which can vary from cube to cube, we use a set of names for the faces that refer to their positions in space. Those names are Up, Down, Left, Right, Front, and Back. In the context of written algorithms you may see something like
R U R' U R U2 R' U2
which cycles the uf piece to the ub position, moves the ub edge piece to the ur position and moves the ur piece to the uf position, and rotates the corner pieces ulb, urb, and urf counterclockwise in place.)
R = Right face 90 degrees clockwise
U = Up face 90 degrees clockwise
R' = Right face 90 degrees counterclockwise (Typically spoken as "R prime".)
After that the only new notation is U2, which means to turn the Up face 180 degrees. You could also write U'2, but unless there's a specific reason to notate a specific direction, this is not commonly encountered. Remember - clockwise is from the perspective of looking at the face.
If you want to undo an operation, you need to do the opposite of each operation, in the reverse order. So, to reverse the move above, you would do the move
U2 R U2 R' U' R U' R'.
To notate a move of one of the middle layers, or slices, of the cube, the letters M, E, and S are used. M moves in the same direction as the L face, S moves in the same direciton as F, and E moves in the same direction as U. You may see other things in move notations, like the small letters x, y, z, and the small letters of the faces. The x, y, and z notations are to rotate the cube around the corresponding spatial axis, and the small letters of the faces refer to double layer turns, so f is a clockwise turn of the F face and the layer behind it. You can get started cubing without all of these small letter moves, but in any event if you want to learn the notation I would suggest bookmarking this page. You won't have to learn all of it at once anyway, so referring to it as needed will eventually give you enough familiarity.
A collection of algorithms that work together to solve the cube is referred to as a method. Instead of talking about what types of algorithms a method contains, methods usually refer to the overall style of the solution (layer-by-layer, corners-first, CFOP) or the inventor(s) of a specific solution (Roux, Petrus, Thistlewaite, Guimond, Waterman, ZZ.) Discussing any specific method may be outside the scope of what I intended, but in general there can be any number of methods. If you're just trying to get the cube back to the solved state, there is more than one way to get there. What algorithms are required depend on the steps we decide to take. Still speaking generally, the steps of a solution boil down to solving some of the pieces and then another group of the pieces, and then another, until all groups of pieces are in the correct locations and correctly oriented. Each subsequent group of pieces typically takes longer algorithms, knowing that we have to not upset the pieces put in place from previous steps. That's not to say that the previously solved pieces never move during the algorithms, you just have to pick algorithms that put the things that are already solved back into place by the end of each algorithm.