How to use Song of the Siren correctly?

 

Retreat

This is most often done when you're split pushing, but also if you take a tower or some situation where you find yourself outnumbered.

In this case, your  Song of the Siren, and back out or Town Portal to safety. At level 16, this spell is nearly broken for being able to split push. It has a cooldown of 60s., which nearly oincides with the cooldown of your  Mirror Image.

Initiation

You use sleep here to keep a bunch of heroes in place while your team sets up. This may be setting up some big AoE ultimate (which takes coordination), or just allowing your team to get in position (e.g. someone is still porting in, or your team is wrapping around to surround them, etc.)

Reset

Sometimes you'll start a fight and realize it is off to a sloppy start. Your team is split up, or they got off some stuns and the fight is spiraling into their control, despite your team having several team fight ults up or a gold/xp advantage.

Another instance is when the other team gets a good initiation on you (e.g. Tidehunter Blink in and ulti). The basic idea here is to give your team a few seconds to recover from the initial volley, get into position, then stop the Song of the Siren and begin fighting on your terms.

Another version of this is done when you want to lock down a kill on a retreating hero. For instance, they are porting and you have no stuns, they are getting away using something like Mirana Leap, or Dark Seer  Surge. You may not be able to get into range to Net them, but you can sleep them and catch them.

Isolation

The last main thing you do with Song of the Siren is isolate heroes. This is the most niche usage and requires either Black King Bars on the enemy team, or good positioning on your behalf.

With Black King Bar - the enemy carry will activate their Black King Bar, you Song of the Siren and because they are magic immune, they are not slept. Your team gets to 1v5 for a short while during  Song of the Siren.

With positioning, you can have situations like you caught the carry out farming alone in the jungle. However, once your team goes on the carry, the rest of their team comes to protect them. You can use Song of the Siren to zone them and basically force them to run into  Song of the Siren, or take a longer route to get to their carry.

To add on, one more much less often used application of  Song of the Siren is for pushes, particularly in the later game where a few seconds of hitting buildings can make a huge difference.

The basic idea is to sleep some heroes while someone/something hits enemy buildings. A few examples:

• Sleeping enemy heroes at/near your base while other members of your team (Lycanthrope, Nature's Prophet) rat away at your opponent's throne. Could be extremely strong if you also cancel Town Portal.
• Sleeping right next to your target building while your illusions/other units/other heroes hit the building. This requires the enemy heroes to be closer to you than the target building so that you can position yourself such that the building is NOT in the sleep range.
• A "zoning" sleep, similar to the above, but more offensive. For example, sleeping behind the opponent's t3/rax, creating a huge zone where your opponents can do nothing. Meanwhile, behind you, your teammates can wail away at the rax. Again, be careful not to catch the target buildings in the sleep.

Lastly, this falls under the usages in the previous post, but  Song of the Siren is extremely effective near the Roshan pit. Even if you can't use it to initiate/reset/etc., you could use it to allow your team to walk in, finish a low Roshan, grab the aegis and leave.