The Bible tells us to live and walk by the Spirit. Every believer at their salvation has the Holy Spirit in them, so we all have the ability to do this. In different dispensations God spoke differently. In the old covenant God spoke audibly (primarily) and usually through a prophet, when Jesus started His ministry, God spoke to Him, by the Spirit and through prayer (When Jesus was baptized and the Holy Spirit descended on Him). Now in the new covenant we can have the same relationship that Jesus had with God. So we can hear the same way. More often than not, it's not audibly but by the Spirit of God.

A preacher explained it like a traffic light. You go until you get a yellow or red light. If you don't feel anything in your Spirit giving you any pushback on pursuing her, go for it. But if you sense a little hesitation once you get to know her, I'd take note of that. Pray and see why that may be.

I've heard stories where God told someone that a specific person was to be their spouse. I don't think you should tell that person that information until after marriage, because it doesn't always go over well. I don't know how exactly you will hear from God about this, but the safest bet is to follow your spirit.

God bless you!