|Almost as easy as clicking a button.|
If another admin from your company posts a status update from the company on Facebook, you as an individual may want to like, comment, or share the post. But you need to make sure you're logged into Facebook from your personal account. If you are logged in as the company, then your like or comment will appear from the company. As awesome as the post may be, the company shouldn't like their own updates. It jut looks weird. (Of course they like it, they wrote it.) If you share the post as the company, you'll be sharing it on the Facebook page it originally appeared and not with your personal friends.
How do you prevent accidentally liking your own page's status updates as the page? Easy. Just before clicking the like button, click on 'comment.' Either your personal profile photo will show up, or your company's. If it's the company logo you're looking at, you need to switch over to your personal profile.
When you're on the company page, about to comment on an update, make sure you're commenting as who you want to. When you click on the arrow, the list of pages you manage will appear, in addition to your personal profile.
Depending on your company and what the Facebook page is for, it may make sense for you to comment as an individual. (Like if the Facebook page is specifically for employees.)
If the page is for consumers, your job as one of the admins may be to help respond to comments made on the page. In this case, you'll probably never need to post as yourself. On the page's settings, you can set the default post attribution to either the page or your personal profile.
Please let me know if you have questions, and share with your fellow Facebook admins so they're doing it right!