There are a number of things you can do, depending on how serious you want to get about it (think about who and what you want to protect against - harassment from other users? Admins?).

Create an account using an email alias or an email account not linked with something you can trace back to your real identity.

If you’re concerned about retaliation/harassment from downvoting something, you could create 2 accounts - one for normal use and the other you only use for downvoting, or one for participating in discussions on controversial topics.

You could retire an account and start using a new one after a period of time, so your entire history isn’t linked to a single account.

The above might be able to shield you from other users but not from admins.

If you want to stay anonymous from admins:

An admin would be able to see the IP address the account uses to connect to the service. If 2 accounts connect with the same IP address and the IP is consistently the same, they’d be able to conclude it’s likely the same person (or someone else in their household) is connecting to the service with both accounts.

If you use a VPN or Tor when connecting to the site, that won’t be as easy to see because many people would connect to the service from the same IP address and the account would likely frequently connect using different IP addresses.

Be aware that if you access the site on a mobile device app with a VPN, it’s possible that the app could contact the server when the VPN is down (for example, if the VPN connection is closed when the device is locked). To avoid that, you could try using using something like OpenVPN with its “Kill Switch” enabled).

Note that the admin of the VPN service would be able to see your connections to Lemmy’s servers (but not specially what you’re doing on Lemmy), so you aren’t fully anonymous. Lemmy’s admins would see part of the picture, the VPN’s admins would see another part, and you’re counting on the 2 not talking to each other (and a good VPN service shouldn’t, unless they’re legally required to).

I use a VPN in general for all connections to the Internet but don’t always care to keep my IP address hidden from some services (banking, primary email addresses, etc - services that will have my personal info anyway). It can be very challenging to keep your IP address hidden over the long haul with a frequently used service - you could end up connecting with the VPN down due to a technical reason or carelessness.

With some services I might have multiple accounts - on one I might not really care if my real IP is revealed, but another on the same service that I’m very careful with to keep hidden.

You could use a browser with protections against fingerprinting like Tor or Mullvad Browser.