I have worked only in 4G network so I can explain how paging work in lte.
Paging and DRX (Discontinuous Reception Cycle) are much related. Paging is used to inform to UE that CoreNetwork has received some data for you so attach to the network to get your data. when UE is in idle mode (I mean there is no radio connection between UE and Enodeb) it enters into DRX mode in which it sleeps(does't read PDCCH channel) and save its battery. After some configured period of time (DRX-config has info) it again wakeup and read PDCCH for P-RNTI(Paging indentifier). Both MME and UE has imsi details. At initial point of time while attaching MME generates UE Identity Index value (see 36.413) with UE imsi. UE also do the same think at its own end. There is a concept of Paging Frame(which radio frame) and Paging Occasion (subframe in side Paging Frame). Paging Frame and Paging Occasion calculation done at Enodeb and UE based on UE Identity Index value value, which is communicated by MME to Enodeb. so UE knows to which radio frame it has to read and which subframe of that radio subframe. In this way, every time Ue wakeup at particular subframe and read PDCCH for P-RNTI and once it validates P-RNTI, it read further for paging-indexity(See RRC paging message). if paging identity is present then UE NAS initiate Service request message in attach procedure.
Please let me know if I am wrong at any place.