After I log in to my Mac air I get a grey screen ???

You have no remaining free space on your computer's storage device. The screen goes gray because the computer cannot work properly until you free up space on the drive. But you can't do that because you cannot start up the computer properly. That means you must erase the drive and reinstall OS X.

If your computer came with Lion or later pre-installed, then do the following:

Install or Reinstall OS X from Scratch

Boot to the Recovery HD:

Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears.

Erase the hard drive:

1. Select Disk Utility from the main menu and click on the Continue button.

2. After DU loads select your startup volume (usually Macintosh HD) from the

left side list. Click on the Erase tab in the DU main window.

3. Set the format type to Mac OS Extended (Journaled.) Optionally, click on

the Security button and set the Zero Data option to one-pass. Click on

the Erase button and wait until the process has completed.

4. Quit DU and return to the main menu.

Reinstall OS X: Select Reinstall OS X and click on the Install button.

Note: You will need an active Internet connection. I suggest using Ethernet if possible

because it is three times faster than wireless.

This should install the version of OS X that you had installed.

If your computer came with Snow Leopard or earlier pre-installed, then do this:

Clean Install of Snow Leopard

1. Boot the computer using the Snow Leopard Installer Disc or the Disc 1 that came

with your computer. Insert the disc into the optical drive and restart the computer.

After the chime press and hold down the "C" key. Release the key when you see

a small spinning gear appear below the dark gray Apple logo.

2. After the installer loads select your language and click on the Continue

button. When the menu bar appears select Disk Utility from the Utilities menu.

After DU loads select the hard drive entry from the left side list (mfgr.'s ID and drive

size.) Click on the Partition tab in the DU main window. Set the number of

partitions to one (1) from the Partitions drop down menu, click on Options button

and select GUID, click on OK, then set the format type to MacOS Extended

(Journaled, if supported), then click on the Apply button.

3. When the formatting has completed quit DU and return to the installer. Proceed

with the OS X installation and follow the directions included with the installer.

4. When the installation has completed your computer will Restart into the Setup

Assistant. After you finish Setup Assistant will complete the installation after which

you will be running a fresh install of OS X. You can now begin the update process

by opening Software Update and installing all recommended updates to bring your

installation current.

5. If you are planning to sell or give your computer away, then do the following:

After you reformat your hard drive and reinstall OS X, the computer restarts to a

Welcome screen and asks you to choose a country or region. If you want to leave

the Mac in an out-of-box state, don't continue with the setup of your system. Instead,

press Command-Q to shut down the Mac. When the new owner turns on the Mac,

the Setup Assistant will guide them through the setup process.

Download and install Mac OS X 10.6.8 Update Combo v1.1.

Step 1

The first step in dealing with a startup failure is to secure the data. If you want to preserve the contents of the startup drive, and you don't already have at least one current backup, you must try to back up now, before you do anything else. It may or may not be possible. If you don't care about the data that has changed since the last backup, you can skip this step.

There are several ways to back up a Mac that is unable to start. You need an external hard drive to hold the backup data.

a. Start up from the Recovery partition, or from a local Time Machine backup volume (option key at startup.) When the OS X Utilities screen appears, launch Disk Utility and follow the instructions in this support article, under “Instructions for backing up to an external hard disk via Disk Utility.” The article refers to starting up from a DVD, but the procedure in Recovery mode is the same. You don't need a DVD if you're running OS X 10.7 or later.

b. If Step 1a fails because of disk errors, and no other Mac is available, then you may be able to salvage some of your files by copying them in the Finder. If you already have an external drive with OS X installed, start up from it. Otherwise, if you have Internet access, follow the instructions on this page to prepare the external drive and install OS X on it. You'll use the Recovery installer, rather than downloading it from the App Store.

c. If you have access to a working Mac, and both it and the non-working Mac have FireWire or Thunderbolt ports, start the non-working Mac in target disk mode. Use the working Mac to copy the data to another drive. This technique won't work with USB, Ethernet, Wi-Fi, or Bluetooth.

d. If the internal drive of the non-working Mac is user-replaceable, remove it and mount it in an external enclosure or drive dock. Use another Mac to copy the data.

Step 2

You might be able to start up in safe mode even though you can't start up normally. Otherwise, start up from an external drive, or else use the technique in Step 1b, 1c, or 1d to mount the internal drive and delete some files. According to Apple documentation, you need at least 9 GB of available space on the startup volume (as shown in the Finder Info window) for normal operation—not the mythical 10%, 15%, or any other percentage. You also need enough space left over to allow for growth of the data. There is little or no performance advantage to having more available space than the minimum Apple recommends. Available storage space that you'll never use is wasted space.