Activate 1.1.1 (OS X and Windows)
From The iPhone Dev Wiki

Activate 1.1.1 on Mac OS X
This is an extract from the 1.1.1 Jailbreak Readme: 
STEP 5: ACTIVATING WITH A NON-AT&T SIM

If you're using an AT&T SIM that will activate through iTunes, skip this step and just activate through iTunes.

To activate with a non-AT&T SIM, we'll need to copy over that lockdownd binary and activation certification we backed up when we were on v1.0.2 and do a little hackery, then copy the v1.1.1 lockdownd back when we're done.

NOTE: In order for afc to start, you must BOOT the phone with lockdownd v1.1.1, so do not reboot the phone during this process. If you have no choice, copy lockdownd v1.1.1 back after, then reboot again to make sure afc comes up.
1. Back up v1.1.1's lockdownd:
cp /usr/libexec/lockdownd /var/root/lockdownd.1.1.1
Now overwrite the iPhone's copy with your old v1.0.2 copy:
cp /var/root/lockdownd.1.0.2 /usr/libexec/lockdownd
And upload the certificate included in this distribution:
scp iPhoneActivation.pem root@[IPHONE IP]:/System/Library/Lockdown/
Now:
killall lockdownd
This will restart lockdownd with v1.0.2's version
2. Download iASign from
http://iphone.fiveforty.net/wiki/index.php/IASign
bunzip2 iASign-v0.2.tar.bz2
tar -xf iASign-v0.2.tar
cd iASign/bin

Overwrite iASign's iPhoneActivation.pem with the one provided in this package
cp /path/to/1.1.1-jailbreak/iPhoneActivation.pem /path/to/iASign/bin/
Now run:
./iASign.mac --automatic iPhoneActivation_private.pem
After a while, it should complete and say "New State: Activated", but it doesn't really work. Don't worry, we're almost there!
3. Now copy the v1.1.1 lockdownd back and restart it:
cp /var/root/lockdownd.1.1.1 /usr/libexec/lockdownd
killall lockdownd
4. << this step should be skipped
It should look like this:
Activating...
InvalidActivationRecord
New State: Unactivated

Don't let iAsign fool you, the phone is now activated.

I would like to report that I have done the same thing with iActivator which has a much better user friendly interface ***
Same steps except Step 4 (not needed). You should use your own 1.0.2 lockdownd as the one in the package is no good.

Activate 1.1.1 on Windows (iASign)
You can use this iASign port http://dl.free.fr/dZt8908BH/IASign_win32.zip and follow the MacOS X instructions using this binary

. BEEEP*
-does not work. there are many ppl who also experience that problem.
>after the first run it says (FactoryActivated) [but still not activated]
>>after the second run it says (Unactivated) [but STILL not activated]
---any suggestions?
--Use the Windows (Online) method, works perfectly for me at 1.1.1. If you dont have a windows PC, try virtualization (if you have Intel mac) until a real method comes for OS X - Beechus
--> If you see a "FactoryActivated" message you're probably using the patched lockdownd. You must replace it by a clean one.

Activate 1.1.1 on Windows (online)
After jailbreaking your iPhone, you will need to activate it, here is how to do this on Windows (STEP 5 of the jailbreak tutorial).
1. First, upload the iPhoneActivation.pem available from the zipped package to /System/Library/Lockdown/
2. Once you're ready to activate, go to
https://ookoo.org/iphone/iasign.php. Follow the instructions on the page to create a custom activator (it's a .exe file which you can download once you've submitted the necessary information). For ICCID, use your AT&T SIM's ICCID (if you have never unlocked) or your own SIM's ICCID (if your phone was IPSF-unlocked in 1.0.2)
3. Note: Do NOT use the iPhoneActivation.pem from the site. Just ignore it since you've already uploaded the correct version in step 1
4. Important: Back up lockdownd (/usr/libexec/lockdownd) and put it somewhere safe (note that this is the 1.1.1's lockdownd). Upload the
original 1.0.2 lockdownd file to /usr/libexec, then open up a SSH commandline window and type
killall lockdownd

NOTE: You will need the ORIGINAL lockdownd file from 1.0.2, not the one patched by PACAY if you activated your 1.0.2 iPhone with it. You can download the original lockdownd from http://www.gofilego.com/download/c73f4591c82747fa03688ad5dd8ec54115443e15
5. Run the .exe file you've generated from ookoo.org. This will activate your phone! (does not matter which SIM, if any, is in the tray)
6. Upload the 1.1.1's lockdownd which you've backed up to /usr/libexec
7. Reboot your iPhone
8. Done! You can continue the tutorial to finish the jailbreaking.
8. Continue with the tutorial in the readme!
Source: http://iphone.simbunch.com/iphone.activate.1.1.1.php