Just use blower or vacuum cleaner to suck out the algae/goo from the outlet of your drain-pipe. all aircons will have this drain-pipe but you gotta know where it terminates.

after that, vacuum away all the water (if there's any) in the drain-pan.

You might want to try a coil-cleaner such as ConCaire (which will further help to dissolve the grime and goo on your evaporator fins, especially if you eat and bring hot-drinks into your aircon room)

Be careful with the vacuum cleaner on the coils, don't bend the fins!

As for explicit details on how to dismantle? Every aircon brand is different... just experiment yourself. You can try to search in youtube