I have an HP envy DV7-7290ez i7 with Windows 8.
How can I set up two-way synchronization for my Gmail calendar with Outlook 2010?
It worked with Windows Vista and my old laptop!
There used to be a utility that Google had created called Google Calendar Sync, but this is no longer developed and isn't even posted on Google's support pages anymore (though you can still find it around the web). Outside of that your best bet is to get one of the many 3rd party applications that are out there to support this. Some of these include SyncMyCal and OggSync. I haven't used either of those.
I use the Google Calendar Sync and it works well (most of the time) as long as you have only one Outlook calendar and one Google calendar. Beyond that it gets a little tricky and buggy (more than normal). It does have issues with repeating meetings and changed/cancelled meetings at times.
How about gSyncit? If you need a really good synchronization tool for Outlook I think you will not find better solution. Unlike Google Calendar Sync, gSyncit can synchronize note, contacts, calendar, tasks with Gmail and others. I use it more than 2 years and all works perfectly. gSyncit has a trial period - try it.