In QGIS 3.0, the snapping settings are accessed through the snapping toolbar.
This is a change from previous versions. In QGIS 2.x they were accessed through Options menu > Snapping Options...
Enable the snapping toolbar through the menu accessed by right-clicking on any toolbar. The snapping toolbar is not available through the View menu in the current version of QGIS (3.0.1); this is a bug that I'm sure will be fixed by the next long term release.
Click the magnet button to enable snapping. Use the other tools on the toolbar to configure your snapping settings. Be sure to set a non-zero value for the snapping radius; a snapping radius of zero effectively turns off snapping.
For layer-specific snapping settings, click the second button in the snapping toolbar. This brings up a menu with these snapping options:
- All layers - snapping is enabled for all layers
- Active layer - snapping is enabled only for the active layer
- Advanced configuration - snapping is enabled for a customizable set of layers
- Open snapping options...
Selecting the option, "Open snapping options...," brings you to a menu, where you can customize snapping settings for each layer.