How do you know the spiritual world is real?
One question you might ask yourself is, how do you know anything beyond your experience is real? For example, some place you've never been? First you might hear about it, and consider whether the source of the information is trustworthy. Did you read about the place in a fantasy novel or in National Geographic? You might ask around to get multiple sources of information. If a picture emerges that sounds reasonable, you might develop a desire to see the place for yourself.
We say spiritual reality can be perceived right now by practice. The spiritual world is a place, and it is also a state of mind. You can be in a heavenly place and feel lousy, or be in a lousy place and feel great. The spiritual world is all around us, and is only hidden from our vision by a curtain made of our selfish desires to enjoy it separately from the supreme enjoyer, Krishna. That curtain is removed by practicing Krishna consciousness.