Accidently emptied a trash bin that contained a very import ant file. How to restore this file?

1. If you simply put files in the Trash you can restore them by opening the Trash (left-click on the Trash icon) and drag the files from the Trash to your Desktop or other desired location.
2. "Time machine" is a built-in backup tool that works with your Mac and an external drive, As the problem you described, I read it. The files deleted in Trash bin could be a different problem which Time machine can't solve. you can read this article and learn more. I hope it will help.
3. If you don't have a Time Machine backup yet, then your best option would probably be uFlysoft Data Recovery for mac software

Mac File Recovery How to Recover Lost Files from Emptied Mac Trash

Don't be panic. The first thing you need to notice is: do not put more pictures or other data in the same place where your deleted pictures were stored to void data overwriting.
Then you can try some data recovery software. You can see
http://www.asoftech.com/articles/how-to-recover-files-deleted-from-recycle-bin.html
It tells the steps how to perform data recovery, including data lost from emptying recycle bin.

Since you are runing under Mac OS X, then you probably need a Mac data recovery software. But the first thing you need to take care is do not put more items to the Macintosh HD where those trashed stuff originally located. Learn more from this article restore Trash Mac for more helpful information. Best regards.

Sometimes you can recover a file depending on whether you have used your computer significantly since you deleted the file.
The following article describes several possible ways to recover items that you deleted from the trashbin
http://www.squidoo.com/recovertrashmac
In the future, I would suggest using Time Machine to backup your mac so that you can access the old versions of any file.

You can restore them from Time Machine backup if you did backup them to it. Otherwise, you need to use a Mac data recovery tool like Cisdem Data Recovery to recover deleted files from Trash bin, hard drives and other external storage devices. Follow this guide: How to Recover Deleted Files on Mac

Don't worry! There is still a way for you to recover your deleted files back (even you've emptied the Trash Bin) as long as you've not rewritten them with any new file on the same drive.
In fact, after the deletion process, these deleted files are not actually deleted. They are still there and become invisible only. That's why you can restore them back. But, only one new file on the same drive would rewrite some of them and make them gone forever. So, you should play attention.
In order to restore them back, you need a third party data recovery freeware that could easily retrieve these files deleted from a Trash Bin.
http://www.geeksdo.com/freeware/data-recovery.html

Note: You should never be so careless to delete anything new on your computer and always remember to back up everything important on separate drives.

Hello,

Mac data recovery software is the best way to recover files from emptied Trash Mac. Recently I had accidentally emptied my Mac Trash containing some important files related to my business and was looking out for a way to recover them. Then I got to know about this tool which really helped me to get all my deleted files. So in my opinion you should at least give it a try to get back your files.

All the best,
Shanky Jacob

Generally, whenever you deleted files, the file itself is not deleted from hard drive but the entries from hard drive directory deleted. And the space occupied by the deleted files can be taken by other files. Therefore, it is possible torecover deleted files from trash.

If you want to retrieve files that were emptied from trash bin, you have to rely on the third party Mac trash recoverysoftware. It is compatible with all Mac operating system like Mac OS X v10.0, Mac OS X v10.1, Mac OS X v10.4, Mac OS X v10.5, Mac OS X v10.6, etc. Besides you can alsorecover trashon Windows.http://www.card-data-recovery.com/recover-trash.htmGet more information from this website.

Don't worry. When you accidentally deleted data from recycle bin or SHIFT+Delete your files. The data itself isn't deleted, just the index entry that tells the system where the data for those files is located. The area containing the deleted data is also now marked as free space so it is available for any new files to be occupied there instead. So Shift+delete won't make data erased permanently.

You may wondering how to recover data? Here are the answers,

If you are using DOS system( not popular nowdays), it's very easy. Just use "undelete" command and your Shift+delete data will be back easily. But I guess it's unlikely you are using DOS. So keep an eye on following assumption.

If you are using OS higher than 2000 or XP, then there is no such undelete command. But you still have great chance to recover the deleted data. And the most effective way is to try a data recovery software. Data recovery programs like Wondershare Data Recovery is very powerful. You may get this program here,
http://www.wondershare.com/data-recovery/index.html

But no matter what operation system you are using, before those shift+ deleted files are recovered, never attempt to put more files to your computer hard disk especially the disk which you deleted files located. Because saving more files may cause original data overwritten. Once overwritten, it's impossible to recover.