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Since Contramuffin answered most of it, I'll focus on the diacritics.
The acute in *ḱ *ǵ *ǵʰ shows that they aren't the same as *k *g *gʰ. Odds are that the ones with an acute were pronounced with the tongue a bit fronted (palatalised).
The acute over other consonants, plus in *é *ó, is something else entirely. It's the accent - you're supposed to pronounce those consonants with a higher pitch. "Yay, consistency" /s
The macron over *ē *ō is to show that the vowel is loooong.
Those floating ⟨ʰ⟩ refer to aspiration. Aspiration is that "puff" of air that you release when you say ⟨pill, till, kill⟩ but not when you say ⟨spill, still, skill⟩. In English this is not distinctive, but in a lot of other Indo-European languages it is, and the mainstream hypothesis is that it was distinctive in PIE itself.
In the meantime, a floating ⟨ʷ⟩ means that the consonant is pronounced with rounded lips. The difference between something like *kʷ and *kw is mostly that the first one behaves like a single consonant, the other as two.
That ring under some consonants is to highlight that they're syllabic, as if they were LARPing as vowels. It's a lot like writing "button" as "buttn̥".
If you ever see *ə₁ *ə₂ *ə₃ etc., pretend that that "ə" is "h₁". It's simply different ways to annotate the same stuff.
*H means "this is *h₁ or *h₂ or *h₃, but we have no clue on which".