Jūrmala is easily accessible from Riga by a six lane highway. However, this highway is paid in summer. After paying Jūrmala entry fee one may in theory park freely there, but in practice those free parking places are often filled with cars in summer weekends.
An alternative is going to Jūrmala the traditional way – by train. It takes from 20 to 40 minutes from Riga depending on at which of many Jūrmala train stops you will exit. While the trains stop at every station, some of them turn around earlier than the Western reaches of Jūrmala so if you go somewhere beyond the center see if your train goes there. The trains are fequent (at least 1 in 30 minutes ar Central Jūrmala, save for nights) and may also be used for local transportation. However, vans also traverse Jūrmala.
Jūrmala is narrow, so basically everything revolves around rail and the main street. However, Jūrmala is unusually long for a city with size, a whooping 31 km in length, making walking and even biking often impractical (if the goal is beyond district). Bike rent, is, however, readily available.
E.g. distance from Majori to Ķemeri spa is 21 km, and from Majori to the skansen at Lielupe – 9 km.