How do I prove something without premises in a Fitch system? If asked “Prove in Fitch: From no premises, derive $A \lor (A \to B)$. Without using Taut Con?"
These are the are the Fitch rules, and this is what I have so far. 
Should I aim to use V Elim to isolate both sides and then derive with the method I'm currently trying? I'm unsure how to piece that part together.

Yuck!  It looks like somebody is trying to give you a headache.
To solve this there are a couple of general tricks you'll need to implement.


*

*derive $\neg (C\lor D)\vdash \neg C$.

*derive $\neg(C\to D)\vdash C$.


Combining yields a derivation of $\neg(A\lor (A\to B))\vdash A\land\neg A$. 
Toward 1, after assuming $\neg (C\lor D)$ you'll want temporarily to assume $C$.  An application of $\lor$-intro gives you a contradiction.
Toward 2, you'll first want to have achieved


*derive $C,\neg C\vdash D$.


With 3 in hand, let's return to 2.  Assume $\neg (C\to D)$.  Temporarily assume $\neg C$.  Further temporarily assume $C$.  After reaching $D$ by trick 3, conditional proof gives $C\to D$.  You now have a contradiction, returning $\neg\neg C$.
Finally toward 3, the strategy is to 'convict the innocent': after assuming $C$ and $\neg C$, further temporarily assume $D$.  Here you can can assert $C\land \neg C$.  Using this proof of a contradiction which begins from an assumption of $D$ you can infer $\neg D$.
