Android tablets (but not smartphones) running 4.2, 4.3, or 4.4 allow you to create separate user accounts for each member of your family. In Android 4.3, you can create a "restricted" profile, which allows you to control permissions.
From your Android device, go to:
Settings > Scroll down to and select Users. Tap "Add user or profile" to create either a normal User profile, or a Restricted profile. Tap on Restricted profile when setting up an account for your child. You'll see a list of apps installed on your device, with on/off toggles to the side. By default, the restricted profile is unable to access any apps installed on your phone. Go through the list and turn on the apps and browsers you are comfortable with your child accessing.
To set parental controls for purchasing apps on your Android phone, go to Google Play, and tap the Play store icon in the top left corner to open the menu. From there, go to:
Settings > Content Filtering (under User Controls). You can choose the maturity rating you'd like to set for your child, and add a passcode to prevent your child from changing it. Next, go to Settings > Require password for purchases, and click on "For all purchases." This will prevent your child from downloading any apps without your knowledge.
Android smartphones don't offer additional significant parental controls aside from purchasing apps, so third-party apps are your best bet to safeguard your phone. Kids Place — Parental Control is a good option — it protects your data, limits your kids to parent-approved apps, and gives you the option to block incoming calls and disable wireless signals. It will also prevent your kids from making phone calls, texting, or downloading new apps.