Look what Wikipedia has got to say in here.
There are many techniques; I know few. But different techniques work for different people like medicines. I will tell you what I know.
What we were taught from the childhood, get up early (at least / about 1 & ½ hours before Sunrise), recite mantras or what you want to remember. This time is told to be very important, as we are fresh from sleep / rest, mind is calm, few thoughts in our minds, etc. so our mind is said to be in a good state to receive. Repeat daily.
I / we remember stotra or hymn by same technique. We use it for other things too, like tables in mathematics (1 to 30), etc. Recite everything what you want to remember daily, weekly, monthly,...once in a day. And, you will remember each word, in sequence. It does work. I wanted to remember one such “stotra”; I started it in Spetember / October 2010. I used to recite stotras in the morning or evening. Now today, I remember each & every word of it, and in the sequence. Today I remember 5 stotras of hundreds of lines, 10 / 12 aarti, and some more mantras. This is very easy technique & as far as I know it applies for everyone.
We often neglect our minds / inner things as compared to outer. We exercise to maintain good physique & health. So should we do it for our brain, mind, and soul. It increases our mind / inner performance, as physical exercise does outer physique.
In ancient India, many books / epics were used to transfer from generation to generation by means of memory. People used to remember them as there was no other way back then; printing wasn’t invented by that time. Schools, called Ashram in those times, were the place where the knowledge transfer used to take place. Children, about 8 / 10 years old, were admitted, taught by their “Guru“s. There were people who were hear for one time & remember it.
Below are couple of links which list some techniques.
Few techniques
Another