Hi Steadyeddie, you don't say where you live on the planet this answer assumes you live in England.

1.onions
You can plant onion sets now or in spring, or sow seed in spring
2.parsnips
spring
3.carrots
spring
4.turnips
spring through early summer if this is the milan turnip
5.swedes
late spring
6.beetroot
spring
7.garlic
now

Yes they can be sown side by side, remember the carrots and parsnips need a fine, sandy tilth, whilst the other root vegetables and potatoes prefer some well rotted manure or compost dug into the soil, onions and garlic appreciate this too.

Use the alphabetical index here;
http://www.thegardenersalmanac.co.uk/Indexes/index.htm
And you will get my advice on the subjects!...Tg

Don't manure the soil where you want to grow carrots though - they'll 'branch'.

Go and buy the veg and herb expert by Dr Hessayon. It's about £10 and available in Smith's. It explains everything very clearly with diagrams! Or take a trip to the local library for a vast array of helpful books for free.

or you could buy this one;

http://www.blurb.co.uk/bookstore/detail/1678421

We all have our favourite books on growing veggies... Teegee's info is a good starting point

Or River Cottage Veg Patch (Mark Diacono) has a nice wipe-able cover (good if you're actually consulting it on the veg plot), some interesting recipes - and is not too daunting!