Offstring yo-yoing (A.K.A. 4A) is a yo-yo playing style where the string is tied to the finger but not to the yo-yo. 1A (string play) yo-yos are often used, as well as dedicated offstring yo-yos. Offstring yo-yos are usually designed with flared body shapes and wide string gaps, to make it easier to catch and land it on the string.
Learning the basics
Before you start
Choosing a yo-yo
Although it is not essential, it is recommended that you get hold of a yo-yo intended for offstring with a large gap to make it easier to land it on the string when you throw. Also, these yo-yos will usually have rubber or rubber-like outer rims, which helps you avoid breaking them or cracking them which can be just as bad (or denting the floor, the ceiling, yourself...) when you miss. Some offstring yo-yos are made out of delrin, allowing for smoother spinning, grinding capabilities, and their ability to bounce straight up off of the floor allow for easier recaptures and recoveries.
To set up your yo-yo for offstring play, hold the yo-yo end of the string in your hand and proceed to wind the string around the yo-yo. You should finish with a yo-yo that has a string wound around but is not tied onto the string. After a few seconds, you can wind without holding the end of the string, then you should be able to throw.
To throw an offstring yo-yo you simply throw the yo-yo upwards, grab the end of the string once the yo-yo has been fully released and land the yo-yo on the outstretched string. Bear in mind that you should not need to throw it too hard, or the yo-yo will go very high and be harder to land on the string. You may wish to learn the throw outdoors to start with to ensure that you don't accidentally break anything when you are learning offstring tricks.
Returning an offstring yo-yo is very similar to a normal sidestyle bind. Once the yo-yo is on the string and spinning, you simply wrap the free end of the string around the yo-yo and pull with your yo-hand and the yo-yo should respond.
Barrel Rolls, Volcano, Regenerations, and Slack Mountain
History of Offstring
Here is an interesting glance at the early stages of Offstring yo-yo play. This is an article that Dave Schulte wrote in 1999 for Yo-Yo World Magazine Issue #4. (the 4th issue was never produced)