How can you have two Google accounts open at the same time? There are several ways to accomplish this. Google actually lets you link accounts so you can switch from one account to the other. I have found this is not perfectly seemless and does not have the same full functions as having two separate accounts open at the same time. Not to mention I can not see both inboxes at the same time, I can only swap back and forth.
The method I use most often is to just use two different browsers. I will open one gmail account in Google Chrome and the other in Firefox or Safari. You can resize the windows so that you can literally have both inboxes side by side.
A third option is to create an incognito window. Go to the file menu and choose New Incognito Window. Go to gmail.com and log into your other gmail, now you have access to both accounts at the same time.