There are two kind of DRX.. Idle mode DRX and connected mode DRX.
In IDLE mode DRX There will be paging occasions(means subframes) and paging SF(system frames). So ENB adn UE knows the occasion and SF. When ever paging message comes from MME , ENb will schedule paging message only in those occasion, so UE will wake up on those occasion and checks for the paging message, if paging comes then it will decode and comes to connected state.
In connected mode DRX, UE will not monitor PDCCH for only following RNIT's (C-RNTI, TPC-PUCCH-RNTI, TPC-PUSCH-RNTI), remaining all RNTI UE will monitor PDCCH even in DRX mode. i.e P-RNTI UE will monitor continously so when ever paging comes UE will decode it. Yes in connected mode there will be less power savings because UE will monitor P-RNTI and SI-RNTI.
Hope u understood...