The best way to learn the uke is to pack your bags and head for Tahiti, The Cook Islands, Rapa nui or the Marquesas and hang with the locals! Like all music in the pacific, the uke is generally learnt from a young age and gradually picked up over time from family or friends. Polynesian music is also learnt and played by ear, so when someone starts singing or playing a song you just listen for the key and play along. If you can play a Hawaiian uke then you should be able to pick up the Tahitian uke a lot faster as the chord patterns are basically the same. The main difference is the lead work and strumming techniques/patterns which take time to master. Kaota from Kanua ukuleles has a series of excellent instructional videos (See below) to get you started.
Strumming: One of the hardest things about playing island ukes is the fast strum. On a guitar or Hawaiian uke, it's usually done flamenco style using all the fingers but with the Island style uke we just use a pick. The first thing you need to do is practice getting a rapid strum action by pivoting from the wrist. You dont need to sit in a freezer to get the right speed, just time and practice. Once you get a clear and even vibrating sound going, you can then start creating different rhythms by flicking the wrist a bit harder on the particular down strum you want to stress. It's the down strums which accentuate the particular rhythm you want. The more advanced stumming rhythms are sometimes similar to Rutu Pa'u (Cook Island drumming) and especially patterns played on the Pate (lead rhythm drum). It takes a while (sometimes years) to get the rapid strum rhythms wired, so just keep at it!
Try some lessons with Kaota Puna from Kanua Ukuleles:
Lessons with Toanui Ruta (in French)
Chord Chart (pdf)