Much like cubeshape for square-1, you can learn which HTR states connect to each other. You don't need to know
every connection, just enough of them to make progress. (And unlike cubeshape, there are only 14 HTR cases, so it's really not that much to learn!)
I think most video tutorials on HTR (including Tom Nelson's, which Spencer linked) don't do a perfect job explaining this, so if you really don't want to learn from a text guide, your best bet is to consult many different videos and fill in the gaps yourself.
I personally used Jay's (text) guide to get started:
https://www.speedsolving.com/threads/fmc-a-guide-for-finding-htrs-once-youve-found-a-dr.87220/ There's also an accompanying video (but it's not really necessary):
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I forgot to address slice insertions! For slice insertions, the two main methods are:
1. RNISS around a bunch of quarter turns and see if you can solve the slice together with it. (Aka the "just look at it and solve" method.)
2. Find some suboptimal slice insertions, then try to simplify by exploiting commuting subsequences. E.g. E commutes with R2 F2 L2, so U2 D' R2 F2 L2 U' can be simplified to U2 D' E' R2 F2 L2 E U' = U y R2 F2 L2 Uw'. This technique is useful for simplifying +2 (or worse) slice insertions, because directly finding +1 insertions can be quite time consuming.
At a basic level, you should pretty much only care about inserting slices that are perpendicular to your DR axis. E.g. if you did DR on white/yellow, the slices you insert will be E/E2/E', but if you did DR on red/orange, then the slices you insert will be M/M2/M'.
Remember that slice notation is
not allowed in your final submission and you'll have to rewrite them as a combination of a normal move and a wide move.
