Not a medical student but oh well
I went to cambodia for 2 months with an NGO in december/january.
My position was a volunteer Occupational Therapist, I worked in an orphanage for children with disabilities (mostly things like autism, developmental delay, cerebral palsy, spina bifida, amputations and sensory processing disorder). Did some OT stuff as well as some behavioural interventions on the children there (I've done a type of behavioural therapy before). As well as helping the kids, I was helping the staff (in conjunction with volunteer physios) learn safe feeding techniques, communication techniques (as the majority of them were non verbal) as well as working on a few other side projects.
I loved the experience! I had so much fun at the organisation, I'm still doing some work for the orphanage on some other projects. For me what the NGO did, was set me up with the orphanage, provide food and accommodation as well as provide help when needed
The application process was pretty easy, just make sure you do a lot of research because there are a lot of 'fake'/shit NGO's out there.
Also make sure that if you go straight to the source. i.e. don't go through some American/Australian NGO that will refer you to some other NGO that will refer you onto some other NGO, because you'll end up having to pay them all money. I met people who were paying over 5 times what I was paying.
You also need to remember that you're not gonna change the world or anything, but you can make a small difference