How do I look after my dendrobium orchid after flowering

I would keep it warm, in very bright indirect light, or filtered morning sun, and a little on the dry side, though dont let the leaves shrivel. Sometime soon, new shoots should start emerging from the base of the old canes, when you can start to increase watering, and start feeding. A 20-20-20 formula has worked best for me.
Once the new shoots are nearly full size, the leaves on last year's canes will probably start to turn yellow, and drop off, so don't panic. Once that happens, adding seaweed extract to the regular fertilizer will help increase the next bloom, and increase the number of new shoots next spring.