Seed packets & gardening books will tell you that February is the time to start sowing parsnip seeds, but I like to sow them in March. It improves your chances with the famously slow & erratic germination, the soil is a little less likely to be freezing cold & sodden, and you don't have to hare about the place getting the soil turned & raked into a fine tilth a month before anything else gets sown. To be honest, you can sow as late as April & still get good results.
Parsnips like a sunny spot with fertile, well-drained soil, preferably light & sandy, but do well in my soil (which is on the clay side of loam). It will grow in heavier soils, but will come out as vegetable Cthulhu's (very forked - but once scrubbed, chopped up & roasted or made into soup, no one will know the difference!). Recently manured soil will also produce vegetable Cthulhu. Stony soil will produce vegetable Cthulhu. Looking at them in a funny way will produce vegetable Cthulhu.
Parsnips grown in the heavy clay of Sheffield - certainly not showbench material, and prone to canker, but they were delicious!
Like most delicious things, they are prone to pests & diseases. Carrot root fly (aka The Little Bastards) can be avoided by sowing parsnips between rows of onion, garlic or chives, or growing in 1' high raised beds, or covering the plants with fleece (I sow carrot & parsnip seeds between rows of shallot & garlic, which seems to work well). Canker (a vague term that basically means fungal disease) is a rusty, brown or black areas around the crown of the parsnip where roots have been damaged by carrot root fly, slugs or being a bit heavy handed when wielding the hoe, and infection sets in. If it's a small patch, you can just cut it off when preparing your parsnips for cooking. If it's more serious, you can try growing resistant varieties (Gladiator & White Gem are pretty good) or improve the drainage of your soil (which is a roundabout way of saying 'Dig').
As vegetables go, parsnips are not really suitable for a small garden. They take the best part of the year to grow, and need very particular soil if you want long, straight roots. But if you can, I really recommend them. Their sweet, nutty flavour is a real pleasure in the depths of winter.
*You know how people say the sound of fingernails on chalkboards cuts right through them? Knives on china plates. Gets me every time.