The quiet time is a hallowed institution in Christian culture. It is also known as spending time in the Word. The phrases "quiet time" and "in the Word" are interchangeable and are exclusive to Christian culture.
Christian culture has lots of handy hints on exactly how to have a quiet time. There are books and websites that tell you how long a quiet time should be (industry standard: 15 minutes on average), when it should be (first thing in the morning is ideal) and what kind of attitude you should have (a good one).
The Psalmists didn't always follow this prescription and in half the Psalms they're angry and railing on about wanting death and destruction for their enemies. To Christian culture, this isn't a very good attitude. But God must have liked these honest prayers enough to make the Psalms the prayer book of Israel.
Christian culture also has a handy acronym to assist you in your quiet time: ACTS (Adoration, Confession, Thanksgiving, Supplication). To them it's an ideal order in which to pray. Interestingly enough, the prayer Jesus taught in the Sermon on the Mount put supplication (give us this day...) before confession (forgive us our debts), and omitted thanksgiving entirely. Work that one out.