request for payment - it's transaction with negative amount
for example:
addr_from = my addr, for request payment
amo = -0.033
addr_to = addr of my client
this transaction not included in blockhain but rertranslated to p2p network
my client receive this transaction and see that in table "requested payments"
https://bitcointalksearch.org/topic/m.7887450
It isn't that easy. People can get spammed, the network can get DoSed, and the person that receives such a request has no obligation to pay. You can simply contact him/her through another way and ask him/her to pay.