To do fully controlled ETTL flash off-camera you need either an Off-Camera Shoe Cord or a wireless device of some sort that supports communication between camera and flash.
Most Off-Camera Shoe Cords are not very long.... only 1 or 2 feet typcially... just long enough to put the flash on a bracket that's attached to the camera. You mention putting the flash on a separate stand, which suggests to me that you might be using a simple PC sync cord to connect the flash to the camera. That will only work in manual flash mode.... no ETTL.
You can get a longer Off-Camera-Shoe Cord custom made (
http://www.paramountcords.com/product-category/sync-cords/ttl-cords/canon-e-ttl-cords/) that will support full ETTL function, but those are rather pricey and will only control a single flash.
Or you can use a wireless controller such as the above (radio type) or Canon's own ST-E2 (optical type). The radio trigger or ST-E2 module fits into your camera's hot shoe, supports most or all ETTL functionality and allows you to control multiple flashes wirelessly.
The 580EXII is designed to work with the optical/ST-E2 controller. (The newer 600EX-RT flash and ST-E3 module use radio.) The third party devices such as the one shown above translate optical to radio and then back again.
Actually, your 7DII has built-in wireless control, even without the ST-E2 module, using the built-in flash to communicate optically with off-camera flashes. It uses a series of flashes of white light from the built-in flash to communicate with the off-camera flash. The ST-E2 module uses a less intrusive, near IR form of light for the same purpose.
Optical control such as this is more limited in where you can place the flash, as well as the distance it's able to reach. The flash's red front panel has to face the optical transmitter and cannot be blocked by an obstruction... and the distance possible is about 30 ft. max.... less in brighter ambient light conditions.
Radio communication either with those third party transmitters and receivers or with Canon's own radio based flashes and modules has greater freedom of placement and works at greater distances. It can work around obstructions, doesn't need to be line of sight and usually is able to operate up to about 100 ft. Maybe more, in some cases.
I agree with some of the previous responses, chances are that you either have the wrong type of connecting cord or have something set incorrectly in the camera. When I've had problems like that it's usually something simple that I've overlooked or misinterpreted.
If you have downloaded a manual for the 580EX, make sure it's the Mark II version since that's the flash you're using. There were a number of changes from the original 580EX.
Is the Off-Camera-Shoe-Cord you're using a Canon or cheaper third party brand? I use three 580EXII (and three 550EX) with both Canon OCSC-2 and OCSC-3 without any problems. I've heard of some problems with cheaper third party, but haven't used them myself. And, I did have one cord's hot shoe loosen over time and with lots of use, causing some problems with connectivity... So I took them all apart, put a little bit of blue Locktite on the screws, reassembled and haven't had any problems since. I use these on flash brackets, attached to the camera or lens' tripod mounting ring. For more remote, multi-flash setups I'm using an ST-E2 (but have seriously considered getting some of the third-party, radio controllers, now that they've come down in price significantly).
Usually when I have any problems, it's something I've set wrong on the flash or on the camera. Flash mode (ETTL), sync speed, "flash off" in the camera menu, etc. It can be as simple as accidentally setting the camera to the "green box A+" super-automated mode, which will override many of the camera settings.
Someone suggested putting the flash directly in the camera's hot shoe and seeing if it works okay... then, without changing any settings, remove it and re-attach using the Off-Camera Shoe Cord. If it will no longer work once on the cord, then the cord is probably faulty.
The printed manual supplied with the 7D Mark II is very abbreviated... it's only about 150 pages. It must omit a lot of info!
The complete 548 page 7DII manual is on the disk provided with the camera... or the same PDF can be downloaded from the Canon website. (There's also a second manual just for the 7DII's AF system, about 50 pages.) The 580EXII manual is available online, too, if needed.
If new to it, there is a helpful,
extensive, three-part overview of how Canon ETTL flash and EOS cameras work together here:
http://photonotes.org/articles/eos-flash/