I can recognize the word 'yaj' in ' vIyajbe', but the lessons don't explain the other words that makes up the phrase so I'm unable to find common words for things like 'no', 'not', or 'do'. Is this just how the language is or am I missing something?
I'm not fully understanding your question. Let me check first that you are reading the Tips & Notes. I feel like all that is explained in the Tips & Notes. But maybe we could tweak the Tips & Notes to explain some things better. Duolingo has hidden the Tips & Notes a little, so if you haven't read them, please take a look and see if it makes those details clearer.
If you are doing the course on iOS or Android, you cannot currently access the Tips & Notes through the app. To access the Tips & Notes, you will have to access the course using a web browser at https://www.duolingo.com/. You can still do it on your mobile device, but you will have to use the web browser instead of the app (or you can do it from a computer). When you click on a Skill, it will expand to reveal a Start button, a key, and a light bulb.
If you click on the light bulb it will reveal the Tips & Notes and give you a detailed explanation of the grammar that is introduced in that Skill. If you have questions after reading the Tips & Notes for any Skills, then please return to the forum to ask your question, explaining what you didn’t understand or what seems contradictory to you.
To add what jdmcowan wrote about reading the tips and notes: the first unit mostly teaches fixed phrases, without expecting students to understand the grammar of the individual bits of words. For example, vIyajbe' is taught as a single word meaning "I do not understand him/her/it".
Later units more explicitly teach (in the tips and notes) prefixes such as vI- and suffixes such as -be'.
There are two attitudes among starting language learners, those who want to know what every syllable means and how it fits with the others, and those who who want to get straight to saying something usable. I find most language courses compromise by teaching a few canned phrases first, and then hinging off the simplest of those for grammar. Unfortunately Klingon lacks a spectrum of Good morning-type utterances, and the grammar of nuqneH and nuq 'oH ponglIj'e' is a little tricky, and I know some learners don't like to be left hanging on how that works.