"I kind of see each one as something new to learn rather than, knowing the concept and being able to apply it in different situations."
Kiss of death in organic chem. Best get the basics before things get away from you.
Start by breaking the words down.
"Nucleophile" = "loves nucleus". A nucleophile is something that is relatively electron rich. Nucleophiles are usually the easiest thing to spot because draw electron density as lone pairs or bonds. These are electron rich sites, and in an arrow pushing mechanism, its where the arrow always starts.
"Electrophile" = "loves electrons". An electrophile is something that is relatively electron poor. Electrophiles can be trickier to spot because they lack electrons. Since in most structures we only draw where electrons are, you're in essence looking for something that's missing. The best way to find one is to look for a positive charge, but not all electrophiles are cationic. Another way is to look for a relatively electropositive atom bonded to a relatively electronegative atom. The electropositive atom is frequently an electrophile: e.g C in a C=O group, H in H-Br, C in H3C-Cl.
Get your text book out and do the practice problems and things will start to come to you.