They do need some time to fit in, but you can start positive based training at the same time.
Is she hungry when you start the training? On My Mind: Clicker Training?What a Concept! | Karen Pryor Clicker Training
Charging the clicker....there are softer sounding clickers too
Can you put the clicker behind your back to muffle the sound AS YOU ARE FEEDING her the cheese/chicken/liver.
Then when she's not bothered by the sound (still behind your back) you can click THEN treat.
Then if she's now figuring out that the sound means cheese/chicken/liver (and it may take a few days) then you can start doing easy stuff.
You need TONS of teeny weenie treats given very frequently. She should be swallowing them not chewing them so you can quickly give more.
More great info ---> Helping Shy Dogs Blossom Using Targeting | Karen Pryor Clicker Training
good luck and bless you for rescuing!!!