Evictions are not impossible right now, it's just a little more difficult to evict based on non-payment of rent. Breach of lease terms (other than non-payment of rent) proceed as normal.
For non-payment or partial payment of rent, the difference is now you must provide them with 15 days notice and a specific form that tells them their rights while the COVID moratorium is in effect. The form says they must sign and return a declaration to the landlord stating they can't pay the full amount due to a COVID related reason, and that they must at least pay a certain % of the rent. I think its 25% right now but it is always subject to change every time the moratorium gets extended. If they don't return the form to you in 15 days, or don't pay the minimum % of the rent amount, you can proceed with eviction. If they return the signed declaration to you within 15 days and keep paying at least the required % amount, you can't. But, you are able to serve them this 15 day notice every payment period, so they have to keep declaring each payment period that they can't pay due to COVID related reasons. If at any point they don't return the declaration, you can proceed with eviction.