Arpeggio is the art of doing a normal chord, but picking the strings in a regular sequence. it sounds hard, but once you have got a pattern, the rest is easy.
Often the pattern needs to suit the songs, and some patterns may suit all songs. This is where your knowledge of what string is numbered what will pay off.
One of my first arpeggio i learnt was plucking 1st and 4th together , then 2nd 3rd 2nd . It took me ages before i could pick the right strings in order, and then even longer before i could sing along with it.
Here is a video of me using it (as a side note, this was done 1 month after getting my first ukulele)
Other combinations are going from highest string to lowest and backup, or pretty much any pattern you want. The limit again, is your imagination!
With picking patterns, you may find it helpful to assign a finger to a string, this means you do not need to look for the strings, but just figure out what finger to pull and when.
Start slow, very very slow. Get the pattern down first, do not speed it up until you can run through repeatedly without messing up.
I found carrying my ukulele everywhere and trying to pick the pattern at the same time as walking, talking, watching TV, or other things, helped me a lot.
Some patterns do not work with some chord changes, they work better with 4 counts per chord style songs, however you can get fairly creative , and so long as you have the right chord, you can pick any string and it will fit in.
You will find that a lot of complicated tablature (or picking) are actually easy patterns once you figure out what the pattern is.
What is tablature you ask? Thats in the next lesson!
Next -> Step 8 - Tablature