Q: how to use airdrop between a macbook pro and my iphone 5S ?

Do you have OSX 10.7 Lion?

http://support.apple.com/kb/HT4783

Note: AirDrop for iOS  supports only iOS 7 devices. You cannot use AirDrop on iOS to share with OS X, and OS X users can't use AirDrop to share with iOS devices.

http://support.apple.com/kb/HT5887

As of now airdrop between OS X and ios is not supported. Could come in a future update when mavericks is released.

Mavericks is released. The feature airdrop osx to ios has noit been included

With the release of Mavericks the closest thing ive seen you can do is go into maps and send directions to your phone.....not sure if thats airdrop or wifi though. Still cool for the 3D cities

its very easy:

with mavericks you have iMessage, so you have to send an iMessage from iOS with the attachment to yourself and open it from Messages on a Mac.

it is kinda ugly, i know, but it does the trick

What a load of rubbish Airdrop is then!

So it won't work between IOS & OSX even with both the new updated versions???

Apple, you are failing very very quickly!

Yes, disappointing.  I was fooled by the appearance of "AirDrop" as well. Hopefully AirDrop will allow iOS-Mac interaction in the future. 

The whole idea of sharing has been evolving.  Although I also still think of sharing as "pushing files" to someone or a device, much of it can be handled by synchronizing with the apps that are used to open them or by saving/uploading files to online services.  You can still push most files using messaging (iMessage/email), which is helpful for sharing with other people who don't have Apple products.

Here are some other ways of looking at the problem of sharing photos/files.

For Apple specific syncing/sharing:

• iCloud works well for snychronizing these items between your Apple devices.  Auto sync items Photos, Pages, Numbers, Keynote, iTunes/music, Notes, Safari bookmarks, and a few other.  You can share videos to iCloud (this will appear in iPhoto and in Photos on your iOS device)
• iMessage/Mail - On the Mac, you can Control click (or two finger click with the TrackPad) on any file to iMessage or Mail a file.  You can iMessage or Mail from any iOS device as well.
• iTunes Match (yes, a pay-for service and it requires an Internet connection) works well for listening to your music from anywhere.
• iTunes home sharing is a good way to see your movies and listen to your music stored on your computer when you are near your computer (on the same network)  You can also sync to iTunes over your home network.

Non-Apple:

Dropbox works very well for photos, videos and files.  It is one of the easiest to use that I've tried.

Evernote is good for taking notes on things and having it automatically appear on any Internet-connected device.

Google Drive is okay, I'm just not as ga-ga with it.

I know this doesn't help you figure out how to use AirDrop, but hopefully it gives you other options for sharing files/items.

While AirDrop doesn't work properly you can transfer photos and videos between iPhones, iPads and any computers using applications such as Photo Transfer WiFi or Photo Transfer App. Find this kind of apps in iTunes Store using Search. There are a lot of them.

Try using "filedrop", it will work between iphone, macbook, windows and i believe ipad as well. It works the same as airdrop. It does cost $.99 on the app store but can be downloaded for free to computers.

The sad thing is we don't have to wait a new protocosl or applications if the bluetooth could be used to send and receive files. All the phones with bluetooth can do that except Iphone.

what is the point of AirDrop then?  Mac to Mac it is flawless.  I wanted to send a PDF of schematics to a coworker the other day and nope...AirDrop would be very useful in that context.  Nice feature but nothing to use it for as we have other ways of sending smaller files.