God is infinite. Now, we should point out from the start that, in one sense, infinity is not a divine attribute per se. As we said about divine simplicity, it does not necessarily tells us in and of itself any specific content about what God is. Rather, it cuts off one possible category for understanding God as unacceptable. Instead of telling us what God is, unfinity tells us that God is not something. Specifically, He isn't finite. There are lots of things that this could mean, so it might help us to start with some of the basics from Scripture.
In the Bible, from time to time we find statements that deny some kind of limit to God. For example, in the Psalms and in other poetic literature we find references to God's works, thoughts, salvation, and various attributes as too much to count. In a famous passage in the Gospels, Jesus denies that anything is impossible for God, implying that there are no limits to His power. We find as we go on that God's love never fails, that His works cannot be measured, that His wisdom cannot be boxed in, etc.
The picture across the Bible is of a God who has no boundaries. Every kind of thing He does and every kind of perfection He enjoys, we find we must articulate them without any hint of limitation. God has unlimited goodness, unlimited strength, unlimited glory, and whatever else we may attribute to Him, we know that it is truly limitless. To realize this is to move further upwards. As we raise our eyes higher to the question of who God is, we find that God has no limits to His goodness, strength, etc. because He Himself has no limits in His very nature. It belongs to God simply as Himself to have no limits. God is infinite all the way down, so that He Himself is whole, unbound, unconstrained, interminable in every respect.
When we think of God as entirely infinite, though, it's important that we mean the right kind of thing by "infinite." There are ways to be "infinite" that don't really fit for God. For example, you might hypothetically imagine an infinitely large body, but this is not what we mean when we say God is infinite. God does not extend indefinitely into space like an endless galaxy, but rather is unlimited by space altogether. He need not extend through it all because He is not bound to it in any way. The same applies to various other ways of talking about infinity. God is not infinite in any way that leaves Him limited by certain categories of space or time or whatever else, even if the limit imposed on Him is one that extends forever. On the contrary, nothing at all limits Him, even in a hypothetical way.
And just as we can learn from the unlimited nature of many of God's words, deeds, and attributes listed in Scripture that God is Himself, in His own essence, purely infinite, so we can descend from this point to find God's infinity applied to every aspect of doctrine. Does God's love have any limits? No. Does does God's wisdom only go so far? No. Can God only answer so many prayers, sort out so many needs, or take in so many considerations into providence? By no means! Whatever questions we might conjure to limit God, the answer to them all will be the same. God is truly and fully infinite in and of Himself, and He is infinite in everything that He is.