By Train (HÉV H5):
This is generally the most recommended and efficient way. I found trains depart frequently, approximately every 10-20 minutes, from Budapest's Batthyány tér station (accessible via the M2 metro line) or Margaret Bridge, Buda side (Margit híd, Budai hídfő, served by trams 4/6). The journey to Szentendre HÉV station takes about 40 minutes. You will need two types of tickets: a standard Budapest public transport ticket or pass for the journey within Budapest up to Békásmegyer, and an additional extension ticket for the section from Békásmegyer to Szentendre. The extension ticket typically costs around 450 HUF (approx. 1.20 EUR), and it's advisable to validate it upon boarding.