While the Tanach doesn't require prayer, all successful religions today do require prayer. Islam, Orthodox Judaism, and Orthodox Christianity all require several prayers per day. So it seems that regular prayer helps sustain a religion.
Islam emphasizes prayer more than any other religion. To fit in with Muslims, you should pray with them. Because Muslims pray silently, you can pray with them but pray to yourself in Hebrew. This allows you to participate in their prayers as a karaite.
The content of your prayer should come from the Tanach but should be organized to fit with the movements of the Muslim prayer. Once you choose the content of your prayer, I suggest that you pray daily in order to memorize the prayer. I pray once per day with 2 repetitions. Here is my prayer: