Since you're likely to be both fit and strong in the quads and calf muscles from cycling, one way to ease into running is to start on uphill dirt or mud. Although it's maybe counter-intuitive, this allows you to use the cycling fitness to get a very good work out while not damaging joints not yet accustomed to the pounding of running.
For example, I've just started running again after a four year break (mainly due to various injuries, both acute and chronic, which needed sorting) and I start with a fairly strenuous uphill walk of about 1km - this takes me from home to the start of some lovely hilly off-road. Once I get to the dirt track (muddy in wet weather - greatly increases the shock absorbing effect of the dirt), I start jogging up a steep hill - gradient is about 20 - 25% for about 800m - and continue on the gentler terrain at the top to recover a bit before running the last climb as quickly as I can. This brings me to the summit cairn from which I walk down back to the road and then either repeat or walk quickly back home on the road. This gives a work out of 40 mins to an hour with about half that time running.
The strenuousness of the running section means that you get an excellent workout in the middle of a longer session and the nature of the uphill offroad work means that you're not slamming your body on flat unrelenting tarmac, so you get the chance to develop the strength control you need for running, which you don't get from cycling - particularly proprioception and balance. The other thing about running uphill is that it teaches you to use your forefoot to land rather than heel-striking, which is what results in so many injuries to runners.
If you're really serious about taking up running, check out POSE running - a technique developed to reduce injuries from bad running technique as well as to increase speed and efficiency. It's much in favour with top triathletes.
The other thing if your joints and muscles feel thrashed after a run is an ice bath. The least masochistic version is just to sit in the bath and let the cold water fill up the bath to cover your legs. In winter the water's cold enough (at least here up north) that ice isn't needed. Sitting there for 5 mins is an absolute killer at the time but the after effect in terms of 'rejuvenation' of the muscles is quite remarkable. You don't have to be Paula Radcliffe to benefit from ice baths
I love cycling but there's nothing to compare with the sense of freedom of running well on off-road trails in fantastic places