Question: I've just pulled some beetroot out of my garden.

I've never cooked beetroot before so would love a few suggestions.

Answer: 
My Russian Flatmate inspired me to try 'beetroot chocolate cake'. The beetroot keeps the cake really moist but without the need to use much butter/oil. It's really healthy and tastes very rich and moist, almost similar to chocolate browny. I made two of them in the last couple of weeks and will make another one tomorrow.
As per recipe, I tend to change mine over time, but as a rough guideline, you can use a carrot cake recipe and replace the carrots with beetroot. And of course add some chocolate :). My cakes both had about 1/2 kg of beetroot in it.
The only way i have beets is roasted with a little olive oil, salt and pepper(fresh cracked of course). I find that if steamed or boiled, the beet flavor gets watered down. Sometimes i make a relish like dish with with the baked beets sliced along with parsely, garlic,onions, and a light drizzle of white vinegar, letting it macerate for a few hours before eating.