Which is the best way to convert Ac to DC , with maximum efficiency possible by using a transformer. The required voltage is 5v and current is 1a . I saw a circuit from my mobile phone charger they didn't use 7805 voltage regulator. They first convert Ac to DC using a bridge rectifier and then to transformer. Their circuit is complicated to understand. Can anyone post a link where I can find a circuit diagram.
Switched mode power supplies (SMPS) are the standard method of doing what you require. They are efficient, compact, light weight and, due to mass production, low cost.
See my answer to How does a cell phone charger work? for a brief overview of the operation and identification of the essential parts of an SMPS.
SMPS design is tricky and since mains voltages are involved they are hazardous and difficult to debug. You will not build one for less cost than a commercially available unit so I recommend that you avoid attempting this until you have advanced well in your electronics studies.