If you want to board a train, you don't try to jump in through an open window while it's moving at full speed. Emacs and vim are very fast trains with very slow acceleration. You're going to spend days, possibly weeks, struggling to do things that were trivial in your old editor as you get up to speed.
If you can't afford that during your productive coding hours, you'll need to set aside dedicated time to be productive at learning - time when practicing vim or Emacs is the only goal. Run through vimtutor or the Emacs tutorial (Ctrl-h t) to learn the basics, then run through it again. Repeat until you can do the tasks without reading the parts explaining the commands.
Grab a random long file of code, make a copy, open the copy in your editor. Practice navigating - pick a character on the screen, work out a fast way to get there without touching the keyboard, then execute it. Practice selecting words, bracket/quote-delimited chunks, lines, functions. Practice making small but precise edits. Get used to the different paradigm of cut/copy/paste that both use, including registers (vim) or the kill ring (Emacs). Practice using searches to move around, and also search/replace.
Learn how to use the built-in help. Both Emacs and vim have amazing help systems that cover every default keybind, built-in command and user-customizable setting.
Do all of the above without any customizations or plugins. After you've mastered the basics, you can start customizing, but try to only do it to fix pain you've already experienced rather than add things you might need some day.