This is for Chromebooks and some newer PCs. It does not work on older PCs. (For Niqud in Windows, see this post.)
If you need a refresher on setting up Hebrew in Google Docs / on a Chromebook, see my post here.
The key (pun fully intended) to doing this is the Alt Graph key, often abbreviated AltGr. Don't panic. You do so have one. It's the Alt Key to the right of the spacebar.
When you are in Hebrew on a Chromebook (Ctrl + Spacebar to switch back and forth), position the cursor after the letter under/over which you wish to insert a vowel. Hold the AltGr (again, the Alt Key to the right of the spacebar) plus the following keys to insert niqqud.
(There's kind of a mnemonic to it - for many of the basic vowels, the key is the Hebrew letter that begins the name of the vowel. So [AltGR +] the ח' key (J) for חירק; the צ' (M) for צירה, the ד' for דגש; the ש' for שוא. The תנועות חטופות are immediately to the right of their counterparts. So פ' (P) for פתח and the [ key for חטף פתח; the ק' (E) for קמץ and the ר' (R) for חטף קמץ; and the ס' (X) for סגול and the ב' (C) for חטף סגול. The ו' (U) is also the dot for the חולם. The backslash \ looks like a קבוץ, I guess.
Since the A is the ש' key, the key to its upper right (W) puts the dot for the shin, and the key to its upper left (Q) puts the dot for the sin.)
Downloadable copy can be accessed here.
