The way, when in person with someone, that I have tried to describe what Evangelical Calvinism is, is to contrast it with what most people think of Calvinism today (as represented by The Gospel Coalition, or more explicitly by the acronym TULIP or 5 point Calvinism). So that is the way I will engage to flesh that out with you as well.
In general Evangelical Calvinism emphasizes and starts from the idea that God is love! We know this to be the case because He has revealed that to us in and through His Son, Jesus. One of my (still) favorite Bible verses is:
"For God so loved the world, that He gave His only begotten Son, that whosoever believeth in Him will not perish, but have everlasting life." ~John 3:16
"7 Dear friends, let us love one another, for love comes from God. Everyone who loves has been born of God and knows God. 8 Whoever does not love does not know God, because God is love. 9 This is how God showed his love among us: He sent his one and only Son into the world that we might live through him. 10 This is love: not that we loved God, but that he loved us and sent his Son as an atoning sacrifice for our sins. 11 Dear friends, since God so loved us, we also ought to love one another. 12 No one has ever seen God; but if we love one another, God lives in us and his love is made complete in us." ~I John 4:7-12
So we know that God is a personal God who does what He does because of who He is, He is love. And we, as Evangelical Calvinists, use this belief to shape everything else that we articulate in regard to how we think of the way that God relates to us.
This means that we do not think that God primarily relates to us through Law, or us keeping the Law (which is the basic underlying premises upon which 5 point Calvinism is based on); we believe that God has always related to us, first, because He simply loves us (because that is who He is). And within that relationship He has provided expectations that He knew we couldn't even uphold; so because He is love, He did that for us too, through Christ (Christ thus has become the end of the Law for all who believe Romans 9:5).
I would submit that the imagery and reality of marriage is the better way to think of our relationship to God in Christ (that's what the Apostle Paul thought in Ephesians 5, and this is a common theme throughout all of Scripture, especially in Revelation). We don't relate, humanly speaking, to our spouses through a set of codes and laws (even though there are expectations within the relationship); no, ideally, our relationship is based upon love (or self-giveness for the other). I think this is the better metaphor (and reality/our union with Christ) to think of our relationship with God through. Richard Sibbes, a Puritan thought so, as did Martin Luther.
So in general, then; Evangelical Calvinism holds that God is Love and thus dynamic and personal. This is in contrast to Classical Calvinism's and Arminianism's belief that God relates to us through impersonal decrees and laws.
Let me know if this post has been accessible and understandable for you.