Vim has a bunch of different modes that you need to understand before we move on.
Normal mode: This is the mode where you start when you open a file in vim, remember this, as you can't just open a file and start typing to enter text. Normal mode is also known as Command mode as this is where you also can type your commands, e.g. dd to delete text.
Insert mode: Insert mode is where you make changes to your file.
Visual mode: Visual mode is a way to select text, so that you can perform different operations on the highlighted text, such as copy it, surround it with quotes, brackets or similar.
Ex mode: This is the command prompt mode, which you enter with the colon (:), this will drop you to a command line at the bottom of the vim window. Note that you need to be in normal mode to drop to command mode.
Insert before the cursor: i
Append after the cursor: a
Insert at the beginning of the line: I (that's a capital i)
Append at the end of the line: A
Open a new line below the current: o
Open a new line above the current: O
Replace the one character under your cursor: r
Replace the character under your cursor but keep typing afterwards: R (more or less constant replace mode)
Change whatever movement, e.g. a word (w), sentence (s) or paragraph (}): c<m> (where m is the movement e.g. cw)
Change the current line from where you're at: C
Change up to the question mark: ct?
Substitute from where you are to the next command (noun): s
Substitute the entire current line: S
Change the case of the character under your cursor: ~ (the tilde sign, works also on visual mode selected text)
Delete the character under the cursor: x
Delete the character before the cursor: X
Delete whatever movement: d<m> (e.g. dw to delete a word.)
Delete the current line: dd
Delete from where you are to the next period: dt.
Delete to the end of the line: D
Join the current line with the next line: J (delete whatever is between the lines)
Undo: u
Redo: Ctrl-r
Undo all latest changes on current line: U
You can use the dot . to repeat the last action you did. Let's say you delete a word with dw, now you can run 5. which deletes 5 more words.
Now combining this with a search and some editing, it's quite powerful:
Search for a text, e.g. /Delete and then hit enter. You will find all the instances of the word Delete. Now press A to append to the end of the line some text (full command): /Delete<Enter>A" hello"<ESC> (search for the word Delete, append " hello" at the end of the line). Now that we have the action, we can repeat that on all the instances by running n. which means, search for the next instance (n) and repeat the last action, e.g. Appending the text " hello".
Yank selection: y
Yank the current line: yy
Cutting text: dd (delete current line into a buffer, can be pasted, also when deleting a single character it's in the buffer ready for pasting)
Paste the copied text after the current cursor position: p
Paste the copied text before the current cursor position: P