Depending on the scope of the problem, it is possible to fix a leaky pipe yourself, if you don't mind a challenge. Because you are dealing with water, and water can cause significant property damage, you shouldn't fix a leaky pipe yourself if you are not sure of what you are doing. If you are not confident that you can fix it properly, you should contact a local plumber. After all, you don't want to make the situation worse.
While there are self-fusing silicon tapes available for low pressure pipes, they are intended as a temporary fix. Ultimately if you have a leaky pipe you'll want to fix it properly to avoid further water damage. If you have a leaky pipe your best option is to shut off your water and call a plumber.
In most cases the best way to fix a leaking pipe joint is to replace the joint. However, this will depend on the nature of the leak and the type of joint that is leaking. When it comes to leaking pipes and joints, your best option is to contact a plumber. A professional plumber can help you mitigate water damage and will ensure your leaky joint is fixed properly the first time.
If you have a burst pipe, shut off the water to that pipe or the main water shutoff valve for your home or buisness. Contact your local plumber to have your burst pipe repaired as soon as possible. A burst pipe can cause significant water damage if left unaddressed.