What are the other ways, besides other web sites?
Assuming you mean 'besides other app stores': people post download links of .apks on all kinds of forums. Or will send them to you through PMs. Or friends of yours can SMS, IM, eMail, Airdrop, Bluetooth, SonicShare, or even Tweet them to you. There are many ways. Often they are meant to help you. But not all of them are. Trouble is you don't know which is which. That's where the Google Play Store and Amazon's App Store come in. They aim to be your 'trusted source' for apps.
Is the Google play store safe because they review the apps before they are included on the site?
The Play Store is safeR. Not perfectly safe. Nothing is.
But yes, they claim to review all apps before they post them.
Some call that censorship. Others call it welcome moderation.