The easiest way to organize your email is to use Labels - these are similar to folders and are Google Mail's way of helping you organize your emails.
Firstly create a new label, to do this down the left hand side click on More.
Next at the bottom of the list of folders click on Create new label.
TIP: If you already have a existing label(s) then you can click the + button next to Labels at the bottom to create a new label without having to click on More etc.
Then enter a name for the label and click Create
N.B. If you already have several labels and you want this new label to appear underneath an existing label then check the Nest label under box and select where you wish it to appear in the drop down box.
Your label(s) will then appear down the left hand side as shown below.
Now you have a label you can follow steps in section below to move any of your emails into this label.
Open the email you wish to move and click on the Move to button (as shown in step 1 below), a pop up menu will appear where you can select which label you wish to move it too (as shown by step 2)
TIP: you can also drag emails on to the relevant label in the left hand panel to move them.
You can then view the email (and any other emails) but selecting the relevant label in the left hand column.