The Jesus prayer is the one aspect of this that is accessible to all Christians. It's great to say it throughout the day as it keeps the mind from wandering and promotes stillness as the Eastern religions also try to do. It's still good to talk to a priest about any prayer rule though, some would say especially concerning the Jesus prayer.Orthodoxy preserves this through the tradition of hesychasm & the Philokalia which you may want to look into if you're not familiar. However I've been advised that these types of meditative prayer practices should only be pursued with the blessing and guidance of an Orthodox spiritual elder as there is danger of prelest or delusion when taken on independently (and from our perspective some of the Catholic mystics certainly fall into this category).
The key I've learned is just to focus on the words and their meaning. Jesus means Savior, and the Christ is the anointed one. You are simply asking our Lord and Savior, sent by the Father, to heal your sinful soul through His great love and thus save us. You don't visualize anything, don't change your breathing, and especially don't seek altered states without an experienced elder.