#1
Where do you put your pick or how do you tuck it away quickly to go from strumming a verse or chorus of a song to doing a fingerpicking part.

Like for example something simple like fast car by Tracy chapman.

I don't like strumming with fingers don't sound right and just hurts and ruins my fingers.
#2
With an electric you can slip it under the pickguard in many cases, acoustics don't have that option. I have a rubber pick holder on my mic stand for changing picks onstage, spares when I drop one, or when I don't need it because I finger pick a song. In a couple of cases I hold it in my lips when I need both in one song.

You can also get a spring loaded pick holder with a sticky thing on back that can be attached anywhere on a guitar but I hate to put anything sticky on my guitars.

If you're talking about onstage, check your local music stores, they should have a rubber pick holder with your name all over it. If you're talking about at home practicing, put it on a table or anywhere...

I would tend to think you're talking about onstage or band practice though, check these options out.

http://www.guitarcenter.com/Pick-Holders-Picks---Pick-Holders,New-Gear.gc

They also make them in necklace and bracelets I just found out...

Musicians Friend has the mic stand version for 4 bucks...

http://www.musiciansfriend.com/picks-pick-holders
Hmmm...I wonder what this button does...
#3
If you're at a show, many singer/guitarists have it tucked into the mic stand. I place it between my fingers.
#4
There's a cut of Joe Pass on YouTube where he does this...Sticks the pick in his mouth. Of course, Joe isn't singing.....
#5
Throw it on the ground. Stop playing and tell someone to give you your damn pick back.
#6
In a single song, going from flat picking to finger picking is easy, the challenge is going from finger picking to flat picking...

I have seen players slide their pick up their hand with their thumb to free up their fingers for tapping, but this still immobilizes your thumb. I am not aware of any techniques where you can finger pick with a pick in your hand in order to switch back and forth easily, although there may be some I am not aware of...

Have you considered using hybrid picking for those parts?
#8
Check out the Shark pick. It's a flat pick with an elastic band that holds it on your thumb, so you can go from flat-pick style strumming to finger style with a thumb pick.

Not a perfect solution but it works.
#9
I've gotten pretty good at flipping between holding the pick with the index and thumb, then sliding it to my middle finger that curls a bit to hold it. I can only use my index and thumb at that point, but it helps in some situations, and is a fair trade-off between using just a pick, or only open hand fingerstyle.
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#10
I have never done this and I'm hardly one to speak on any topic of advice, what about this.

attach a magnet to the side of your guitar, and use a metal pick?