The best time to practice is early in the morning before you start your day. The mind is clear and there are fewer distractions.
Decide on how long you want to practice, and set your alarm clock to allow you to have finished practicing by the time you would normally start your day. Then all you have to do is get up and go. You will soon find that not only you don't need the extra sleep, but that by the time you have finished, body and mind are clearer and more energised than if you'd stayed in bed.
If early morning doesn't suit, choose the time that fits best into your schedule, but make sure that it's at least three and preferably four hours after a meal, as yoga must be practiced on an empty stomach.
Also make sure that you won't be disturbed while you are practising: turn off your mobile phone, and tell the kids, partners or house mates to leave you alone for a while, pratice is a solitary activity (in the Paññā Sutta, AN 8:2, the Buddha lists seclusion of body and mind as one of the eight conditions for the arising and development of wisdom, and the Hatha Yoga Pradipika also insists on seclusion as a condition for success in yoga).
Beginners should aim for a 30 min practice, or may be a bit more if there's plenty of time, but should avoid being too ambitious. As you progress, your practice will naturally lengthen.
Regularity is the key to success. It is best to aim to practise every day, although taking a day off once a week may be beneficial.
If you are sick or injured, you will need to modify your practice routine to accommodate your condition, and may need expert advice on how to do this, but always try to do as much as you can. This will speed up your recovery.
Women can also take the first few days of their period off, especially if bleeding is heavy, or at least should do a modified, quieter practice and avoid all inversion and strong backbends during that time.
Ideally, you'd have a room in your house dedicated solely to spiritual pursuits, but for most of us, this isn't be possible. All you need, really, is 8'x4' (about 3 sqm) of clean, level floor space in a properly heated room.
If practising outdoors in warm climates, avoid direct sunlight.
Don't wear socks, and make sure no one is watching.