How do you drum up activity for your discord server?
To increast the activity of your discord sever it is recommened that you host events and giveaways, have all sorts of activities. Scheduled activities tend to do better than unannounced activities.
Help me use bots to make my discord server more popular. I want to make my server look more populated and active. I also want to use bots to spam other discord servers to get more real users for mine.
To make your server look more active, the best way is to catch the eye of new users, and convince them to participate in your channels by providing value. 
You can certainly use bots for that. For instance:
- Bots for handling welcome messages, informing new users of your server rules, and prompting them to introduce themselves in a community channel
- Bots that allow users in a voice chat to listen to their favourite music tracks, for instance in a channel devoted to a study room, when users can gather even when they are doing other things in real life.
- Bots for mini games, e.g. those related to card collecting games, so that users can have fun when connected to your server. However, note that those should be restricted to separate channels, to avoid unnecessary clutter.
- Bots for memes, allowing users to create new memes and use them to react in a chat.

However, you cannot spam other Discord servers to get more real users for your own, since this is against Discord Terms of Service, and may get you (or your bot) banned from the platform. Moreover, you cannot invite a bot to a server for which you do not have the Manage Server permission, so you cannot make your bot join all the servers you want.

As an alternative, consider one of the following:
- Many Discord servers have channels devoted to advertisement. You can use those to grow your own server, but make sure to abide by their rules.
- There are bots you can use for advertisement. You can add these bots to your server, and give them permission to send messages within a channel. By doing so, your server will be advertised in all other servers that have added the same bot. In exchange, you will receive advertisement for other servers in the channel the bot has access to. In this way, everybody wins!