Twante is the most accessible delta town from Yangon and makes for a nice half day or full day trip. A short ride on the Dallah ferry from the Pansodan Street Jetty on Strand Road US$1, 10 minutes, and then a bumpy 40 minute ride on a pickup 300 kyat through leafy villages and large pools of water gets you a good feel for life on the delta.
A slower way is by ferry from Yangon 2 hours, US$1 and, for a good look at delta life, consider taking the Twante ferry one way and the pickup/Dallah ferry on the way back.