The Daily Examen (of Conscience/Consciousness) comes from Ignatian spirituality. I've heard some people suggest it's one of the most important parts of our day if we want to grow in spiritual maturity. The idea is that you look back over your day with God and talk about what you see, thanking Him for various things that happened that day, confessing your slip-ups and asking for God's help to be more loving and faithful tomorrow. It's also about asking the Holy Spirit to help you notice things - how God used you that day, how God spoke to you through others, how you walked past that person without stopping to help them, why that situation or conversation upset you so much... Sometimes people explore the best and worst parts of their day, asking God and what He wants to say about / through those situations.
People do this daily review with God in different ways. The most common is to do one each day towards bedtime. I expect some have a more formal approach to it and others a more informal approach. Some might write in a journal as part of their examen. In general I've heard that 10-15 mins is the right kind of length of time to set aside for it.
Personally I do mine in quite an informal way in the early evening once I've had dinner and finished washing up. I sit on my sofa with a cup of tea and talk with God about my day as if I was talking to a best friend or husband or parent. It really is a powerful and Spirit filled form of prayer. I suppose it's a kind of 'listening prayer' at a deep level - noticing how God is intimately involved in the events, conversations and emotions of your day...
Here's a link to a Youtube clip on the Examen: https://www.youtube.com/watch?v=rHQOcRqc758
