This will only work offline now due to the beta hasn't started but I've found the download links and I'll tell you how to play!
Okay first the download locations. Download from Blizzard US - Download from Blizzard Europe
I've updated how to play more efficiently. The old method is still below.
1) Make sure you downloaded the client from above and install. If you get any errors be sure to remove any old Starcraft 2 Beta files on your computer.
2) Download the Map Pack for updated maps AI improvements. Extract once downloaded. Click Here to Download Map Pack Antiga Shipyard.
Antiga Shipyard is provided with different computer AIs. The default one is BNET AI very easy which can be very easy and boring. The other ones are based on Green Tea AI with four levels of difficulty without resources cheating. GT AI Hard is similar to a gold/platinum human player.
3) If experienced with opening the maps go ahead and play or else more steps below to walkthrough the process.
4) Open the Starcraft II Beta Map Editor.
5) Open a HOTS Beta Map from the modified Pack.
6) Click YES when the dependency box appears.
7) You might have to adjust some of the Map > Player Properties to select your race and computer opponents.
8) Also adjust the File > Preferences for Game Speed settings.
9) Go to File > Test Document to play.
If an error pops up just uncheck the box!
Now if you were in the Arcade 1.5 beta you must clear the cache and uninstall any remains of it.
Now the beta is installed to play offline you open up the map editor. Ai opponents can be added by going in to player properties and change players to AI, set their difficulty and even their race. You can also give them a head start in tech or units, anything you want really. Just make sure to add their starting points to a map or use one with them added.
In the editor just load from there and you are able to play the beta before the servers come up.
If the above doesn't work try these steps.
1) Download MPQEditor Link
2) Open it
3) Open the swarm files (Swarm.SC2Mod) and extract them to a temporary folder (1 by 1 or else it will lose data because the mqp editor doesn't seem to be fully compatible with these files, some files will ask you to overwrite I hit no to everything)
4) Open the editor, New -> Mod -> WoL dependency. Save As, file type "SC2Components", hit save
5) This will create a new folder. For me it's StarCraft II 2012 Beta\Mods\merge.SC2Mod (folder)
6) Paste your extracted contents (step 3) in this new folder
7) Reopen the editor, open the merge.SC2Mod folder (for me it created some errors but it ended up okay)
8) Save it as .SC2Mod (file), this will take a while
9) In the editor New -> Training map -> Custom -> Modify -> Add other -> merge.SC2Mod (file)
Here is a look at merging.