Shravan month is very auspicious month in Hindu Calendar. The whole month is dedicated for Lord Shiva worship.
There is great controversy to mark the 28 days window of Shravan month. Purnimanta cycle considers full moon to mark the beginning of lunar month and Amanta cycle considers new moon to mark the beginning of lunar month in Hindu Calendar.
In North India, Purnimanta cycle is considered for lunar month reckoning. It is un-written and undocumented why and when North Indian calendars shifted lunar cycle 15 days ahead of Amanta cycle. Purnimanta cycle might be good for civil purposes but for religious observations, it might not be appropriate, as it shifts the religious window of lunar month by 15 days.
In Purnimanta cycle, lunar year might begin before the Meena Sankranti (which is the 12th and last Sankranti in calendar) which shows that Purnimanta cycle has obvious flaws. However, in Amanta cycle, lunar year always begins after Meena Sankranti and just before Mesha Sankranti. Hence, according to Drik Panchang, following Amanta month cycle to observe Shravana month looks more appropriate.
Astrologically also, most books consider Amanta cycle for lunar month reckoning. Even, most books written on Shravan Mahatmya, i.e. on the glory of Shravan month, assume Amanta lunar cycle to describe all rituals followed during Shravan month. Except Hindi belt in North India, other states like Gujarat, Maharashtra, and most eastern and southern states follow Amanta lunar cycle to observe Shravana month.
Every Tithi during Shravan month is considered highly auspicious to observe Upavas. Each lunar day during Shravan month has been marked to perform some or other Vrat and Puja rituals.
Apart from following Puja schedule based on lunar Tithi, one can follow Puja schedule based on weekdays during Shravan month.
In modern India, all Shravana Vrat and rituals are not followed as per religious books. However, few austerities which are suggested during Shravan month are mentioned below.
It is also important to understand that Puja done for other Gods during the Shravan month pleases Lord Shiva as well. Hence, Puja done for any other Gods or Goddesses during the holy Shravana month reaches to Lord Shiva.
Agastya Arghya is significant ritual which mostly performed during Shravan month. The day, when Agastya Tara rises after getting set for couple of months, is considered very significant. Offering Arghya to Saint Agastya on the first day of Agastya Tara visibility is known as Agastya Arghya.