Step 1
Go into the map editor timing section and find the offset point
Step 2
Tab over to audacity and hit the record button [R] and switch back to the editor for osu! and hit play (Be sure to run osu! on unlimited fps while doing this).
Step 3
You only need a little bit before and after the initial offset, sometimes you may have to check other parts of the song, it's best to find parts where it's silent before the slider ticks in the timing section. Shrinking the height of the track makes it easier to read and use "Selection tool" to measure. the Below you can see the map is 15ms off, we need it at 22ms off so locally we have to use +7ms to play. Why 22ms? When you go to play a -22ms local community offset is applied. It takes a bit of practice measuring and correcting the local offset because sometimes it's hard to read where exactly the sound is. It sometimes helps to change the actual map's offset so you can get a better reading (just be sure to add it in when you go to calculate the local offset)
A local offset you use wont always be the same for someone else due to computers having different timings.
About double time
From what I've gathered the double time offset is incorrect when played. In the image below you can see the track above is played with double time Auto, below it is played with just auto. Tacking on a local offset of -5ms offset should help when you get the offset from the above method.
