Do you know how to convert between context free grammars and push down automata? If so you can use this algorithm:

2) make every state an accept state to create PDA2

This is just off the top of my head - it may be simple to go from grammar to grammar directly. 

 My suggestions aren't correct. This has some suggestions: 

https://math.stackexchange.com/questions/2867376/are-context-free-languages-closed-under-taking-substring

Let $L$ be context free and $\Sigma $ an alphabet

Define $s(L):=\{y \in \Sigma ^*\mid \exists x,z \in \Sigma ^*: xyz \in L\}$

Is $s(L)$ context free ?

I haven't been able to find a counterexampl...

Are context free languages closed under taking substring?

 gives a workable idea by introducing 'colored' alphabets and intersecting with a regular language to erase zero or more characters from the beginning and end of strings in L. I'm not sure how to implement the intersection with a regular language in the rules of the grammar but the other parts seem not too difficult.

I remember less about PDA than about CFG; is the idea that you will accept any prefixes of accepted words, because it will accept a part of the word even if we stop halfway through? but what about substrings that aren't prefixes?

Why would that lead to us accepting all substrings (and only them), though?

Thinking about it more I think both these suggestions are wrong

isn't it just as simple as making every production rule of the CFG also terminal? e.g. if you have a rule:

it's been a while since I studied this stuff so I may be missing something.

Given a context-free grammar that generates a language L1, how do I create a context-free grammar that generates a language L2 whose words are substrings of words from L1? I'd appreciate an exposition I can actually understand

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