First, something I wrote on これで, which applies to それで as well:
As @Belthazar mentions, 腕ならし is similar to 肩ならし. I believe ならし is from the verb 慣らす, mean to accustom (oneself to doing something), or to train (like training one’s ear for music).
Big Sis had just said she can teach Makoto a simple spell. This is what she’s refering to when she says それで (the “that” in “with that”).
- それで = with that (spell I’ll teach you)
- 腕 + ならし = build up your skills (in its connective い form)
- しとこう = (to put into the state of)
That last part is する (to do) in its て form (して) + おく (with the お dropped) (to put in place). You’re doing something, and putting it in that state where, and it remains in that state. Since it remains in that state, it can be accessed in that state later, which is why dictionaries give the meaning “to do in advance / to leave in the current state expecting a later change”.
In this case, Makoto can use the spell her sister teachers her to build up her skill training. Afterwards, Makoto will remain in the state of having her skill trained. (She won’t lose all that training afterwards. Hopefully.) And then from that trained up skill level, she’ll be able to work on her magic further later.
I might translate the line as:
“With that, you can build up your skill.”
But “build up your skill” is a bit clunky in English, so we may want to simplify it to “practice” or “train”.
“With that, you can practice.”
However, “with that” being at the front of the sentence is a bit awkward in English, so let’s move it to the end.
“You can practice with that.”