How do metals transfer positive charge if the protons are immobile? From my textbook:` "When you touch a positively charged object charge spreads over your body."
My understanding is that the protons in a solid conductor are immobile since they are contained within the nucleus, and the electrons are the mobile charge carriers.  How, then, is positive charge transferred? Wouldn't it make more sense for electrons from the neutrally charged object to move into the positively charged one?
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 A: If there is a relative absence of electrons on the nuclei then this absence acts as if it were a positive charge. In fact, the absences can even sometimes behave like bona-fide particles; they are called "holes" in semiconductor physics.
It would make a lot more sense if electric charge were the negative of what it is. Sadly, that is not likely to happen without a completely new unit system, and because you can treat a relative-absence like a charge, it's very, very common for books to simply say "the (positive) charge flows like..." rather than "the electrons carry their negative charge in a flow like the opposite of...".
A: *

*A neutral material has equal amounts of positive protons and negative electrons. 

*A negatively charged material has more electrons than protons. 

*A positively charged material has less electrons than protons. 


No matter the charge carrier itself, the material can have an excess or a lack of them. 
As the other answer mentions, a missing electron (in a therefor positively charged material) can be thought of as a hole. The atom will have more protons than electrons, since one is missing, so it has a net positive charge. If there is such a hole in a metal, then the neighbour electron might move into the hole. This electron thus leaves a hole behind. Then the hole has "moved" to the neighbour location. In this way a hole can propagate through a material in the same manner as an electron. Therefore such holes can be considered "particles" or positive charge carriers moving like electrons just with opposite charge. 

When you touch a positively charged object charge spreads over your body

Touch a positively charged object (which has a lack of electrons / an excess of holes) and electrons from your body move to the object to fill the holes. This leaves holes behind on your body. Therefore you have acquired a net positive charge (a lack of electrons) just as the object started with. 
We often say that a positive charge is acquired, even though it actually is negative charge that we have lost. Usually when talking like this about charges acquired we don't care about what exactly the charge carriers are. In some cases they are electrons, in some cases holes, in some cases charged ions, etc. Usually that is not the important point, when we are only interested in the resulting net-charge.
