How long should my child practice for?
The most important part of practice is the repetition. For most beginners it's best to think of playing each piece through at least three times rather than setting a time limit.
How many times a week?
Four or five different days.
How can I encourage my child to practice?
Decide which days and times to practice and make that part of the daily/weekly routine. I am often told by a child what they do before or after school on different days but this rarely includes playing their instrument.
Make sure their instrument and music is easily accessible. If possible leave it set up and ready to play with the music either on the stand or nearby.
Keep anything that may distract them to a minimum, that includes noise.
Be encouraging whenever possible. Remember it takes time to make a good sound or to play a piece correctly. Simply sitting a listening to them play can be really effective.
Set a target and have a reward scheme. Include bonus points for going beyond the target. For example if your child plays their piece 3 times they receive a point with a bonus point for each extra repetition and for practicing on different days. Have a reward for achieving a certain number of points.
Finally.
Although the above suggestions take time an effort they are very effective and as time goes by they become part of the routine.
For any child under the age of 10 to practice without prompting is very unusual. They rely on adults to remind and encourage them.
The reward for the parent is the joy of seeing and hearing your child progress.