How do you prevent cat from urinating or spraying outside the box what could be the reason for this act.?

There are three huge questions that need to be considered.

First and foremost, is the cat unaltered? An unfixed cat is much, much more likely to spray. It is highly recommended that you have your cat spayed or neutered (it is also a good idea to get the cat blood tested, just to make sure that it isn't a rare case in which the cat may be allergic to sedatives given for spaying/neutering). If you have multiple cats, this is far more likely.

Second, is the box clean? People often underestimate how often a litter box should be cleaned. Litter boxes should be cleaned every single day, multiple times a day if you have more than one cat. It is good to get in the habit of scooping a box every time you see it has been soiled, and replace -all- litter at least once a week (twice a week is acceptable for clumping litters).

Third, does the cat know where the litter is? A cat will not "sniff out" a new litter box, especially if it is just starting to be trained. Make sure that your cat knows where the box is. Also, try not to put it as far away out of sight as possible. Keep it somewhere where the cat may be frequently, and put the cat in the box to make sure it knows where the box is at. Also, cats tend not to prefer closed boxes (ones with lids/covers). A simple litter pan is most effective.

If you keep your cat's litter box very clean, and it still does not use the litter, try switching to a different time. Cats often do not like strongly scented litters. It's nice to keep the smell down, but, a cat's nose is even more sensitive, and it may be overpowering for the cat.

Also to consider is stress. Cats will urinate/spray to mark territory, but also because they are feeling imposed upon. A good product for this is Feliway, a pheromone based product that uses pheromone's that make a cat happy, to put it at ease. It even helps multiple cat house holds to maintain peace- and helps curb the fighting between cats (although this is not guaranteed, of course). This is a very safe product that will not effect you, your cat, or even other house-hold pets such as dogs. Simply spray it where the cat sprays/urinates, and keep using it for 2-3 months. If the cat completely stops urinating outside the litter, you may try decreasing how much you use Feliway, and eventually stop using it all together.

Last but not least, always consider that your cat may have a health issue. While this isn't as common as the other reasons, it is still important to take into account. If your cat urinates excessively, seek veterinary advice and assistance.