On the front end of your community, moderators can moderate your site depending on the permissions that you have given them to do so. Moderation can be done at an item level, or the level of its container. For example you may moderate individual posts from the topic screen, or moderate topics from the forum screen.
Whilst within a post or topic, if you hover over the topic or post you wish to moderate you will see a checkbox appear in the top right of that item. Selecting this will add this to the items that you are currently moderating. Once you have selected at least one item, you will see the moderation menu appear at the bottom where you can select the action you wish to perform. You can see this in action in the animation below.
Within each item of content you will see a moderator actions menu. You can perform similar actions from here, and also see the moderation history for that particular item.
Depending on where you are within the system, the moderation menu will show different actions. Below is another example where posts in a topic are being hidden from the end user.
In IPS 4, deleted is truly deleted. Only give this setting to someone who you are happy to allow deletion of content from your community.
In some of the other areas of the community, you may find moderator actions under a button, such as you can see here in a gallery image.