God can and does speak to us in a whole variety of ways, but most commonly God will speak to us through the Bible - which is, after all, God's word. The more of the Bible that we have in us the more opportunities we give God to speak to us.
Of course, as is the case with any spiritual discipline, the goal of memorising Scripture is not simply to know lots of verses off by heart. Just as the purpose of reading through the Bible in a year isn't about ticking chapters off a list. It's not about learning the Bible off by heart as much as taking the Bible to heart. Memorisation should be accompanied by reflection and application and prayer.
Back in the 1990s I spent a year teaching in Kenya during which time I came across The Navigators - a Christian organisation that works with secondary school and university students, sharing the gospel and making disciples. They had lots of helpful illustrations including this one about the Bible:
This was where I first came across their Topical Memory System - essentially six sets of twelve cards with verses arranged in themes. The cards are designed with the intention that you carry them with you for easy reference and review as you go about your day.
My first set was pickpocketed on a bus in Nairobi!
Now, cards have been replaced with a whole range of apps that help with the memorising process.
If you're looking for somewhere to start have a look at the Fighter Verse app
