Welcome to Android Central! Permissions are necessary for many apps, depending on what they do, so to a large extent, you have to trust the developer. Ways to protect yourself include:
1. Install apps only from legitimate app stores like Google Play Store or Amazon Appstore. Avoid downloading APK installer files from filesharing sites, because those might be corrupt, pirated, or malware.
2. Read the app description carefully--good developers will often explain why certain permissions are necessary.
3. Read through the reviews--apps that have been installed hundreds or thousands of times, with generally good reviews, will be less likely to have nefarious intentions. That being said, be careful about "fake reviews" submitted by the developer himself or herself--these reviews often seem very similar to each other in wording or structure.