1)To increase the volume of your music,i suggest you use some decent music software like audacity to boost up the volume level of your music files.But make sure you do not boost it to high it will sound scratchy and distorted and you could damage your psp speakers and cause a problem as you have to get the speakers repaired.
2)Get a ear bud a gently clean out any excess dust or dirt in the speaker hole.Cleaning helps the speaker to produce more sound by unblocking the blocked sound waves.
3)Buy some really loud external add on speakers like from brands such as logitech's docking station.The negative point of buying psp speakers is you will need spare battery's were ever you go because they take more power to produce more sound quality and loudness.Speakers that can be used with the psp itself are available in many good leading gaming retailers or online and usually in the listed accessories range.
4)Ditch Sony's current music player with the homebrew player called light mp3 its great and packed with many features including volume boost and customizable themes.It has a special option to let you increase volume boost,turning the volume boost too high can mess up and damage your speakers or headphones so be careful!This is currently the only music player for the psp that has the volume boosting feature and is free to download.You can not run and make this application work if you have not installed custom firmware onto your psp such as mm3 or gen d2.The stable version of light mp3 is version 1.2 at the moment.Many people who have ran this application on there psp stopped there speaker from working again!
5)Remove your umd drive door and replace it with a powerful speaker,doing this modification will make the sound have more bass and clarity.The speakers that come built in the psp are small and can't really produce loudness and bass.Below is a instructed video tutorial that will show you how you can mod your psp.You can currently modify the psp with a speaker placed in the umd drive on the following models: 1000,2000,3000 but not the psp go because it has no free space to install and fit the speaker as Sony designed it really small.