There is already a question on whether or not yoga and other non-Christian meditative practices are permissible according to the Eastern Orthodox Church, however I was wondering if all forms of meditative practice are discouraged or whether things like lectio divina, Taize prayer or christian meditation are smiled upon?
The current usage of the word meditation is strongly linked to buddhist/zen/hindu practices of sitting in a certain position, breathing in a certain way, focusing on emptying the mind and ultimately altering one's consciousness.
That kind of meditation and any other spiritual practices from other religions are strictly forbidden by the Orthodox Church for obvious reasons: being a christian and meditating is like being a buddhist and praying to God.
However, the word meditation itself is not imported from asian languages, like samsara, nirvana, chakra, karma etc. It comes from the latin meditatio meaning to contemplate, to ponder. So its original meaning was different, not linked to asian spiritual practices.
One of my friends started his conversion to Orthodox Christianity after reading a book called "Orthodox meditation". He picked it up with exactly your question in mind: Do the orthodox christians also meditate? thinking of course, about the current connotations of the word. In this book, he found out that orthodox meditation has nothing to do with the asian spiritual practice.
The Philokalia, a collection of eastern orthodox writings about the hesychast tradition, abounds in the use of the word meditation, which is used, of course, with its original meaning e.g. in order to attain humbleness, one should meditate on God's infinite powers as often as possible (not a direct quote, just an example I made up).
As another user advised, it's better if you talk to your confessor priest about this, he will tell you whether doing this is beneficial to you or not and give you the proper instructions on how to do it right.