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

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

Answer: 
I like them steamed: Steam , unpeeled, for around 35 minutes depending on size. Use paper towel to rub off the peel after it's cooked, and then slice.

They're very likely to stain your nice towels, clothing, and counter-tops .... a cutting board is recommended.
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.