Sri Sri Vishwa Priya Theertha Swamiji has given very clear instructions on how one can chant the Vishnu Sahasra Nama.

• In case one is not able to chant all the names at one go, it is perfectly ok to chant how many ever names can be done in the time we allot for it. One should not, in order to finish the entire stotra, hurry up and mispronounce any name.
• One should be “awake” and “aware” while chanting the names. There are many places in the stotra where laxity can mean that one either jumps several shlokas and goes ahead or rewinds and comes back several shlokas. Such a mistake can lead to the stotra finishing very soon or not finishing at all!
• Special attention should be given to pronunciation.
• If the first letter of the next name starts with “Sa”, “Sha”, “SSha” or “Ka”, then previous “Visarga” (two dots) must be stressed upon and not spelt completely. If the previously mentioned letters are not present, the Visarga must be converted to “O” and the names must be pronounced continuously.
• Long vowels must not be shortened in a hurry.
• Vishnu Sahasra Nama, technically, starts with “Vishwam Vishnu….” and ends with “Sarvapraharanayudha”. If one starts with “Vaishampayana Uvacha …”, it brings special merits. But there is no harm if one starts directly with “Vishwam Vishnu..”
• Those who have had Upanayana Samskara done should use “Om”. Others should use “Sri”.
• The chanting should be started with the following prayer
•               Asya Sri Vishnordivya Sahasra Nama Stotrasya
•               Bhagavan Veda Vyasa Rishihi
•               Anushtup Chandaha
•               Vishwarupi Sri Maha Vishnurdevata
•               Sri Mahavishnu Prasada Siddhyarthe Jape Viniyogaha