Identify the Damage: Check for broken, cracked, or missing slates. Also, inspect the roof for signs of water damage, moss, or lichen growth.
Check Flashing and Gutters: Ensure that the flashing around chimneys, vents, and other roof penetrations is in good condition. Gutters should be free of debris to prevent water backup.

Use Proper Equipment: Ensure ladders are stable, and consider using roof jacks for a secure footing. Wear non-slip shoes and a harness if the roof is steep.
Avoid Walking on Slates: Walk on the roof as little as possible. When necessary, step on the roof battens or use plywood to distribute your weight.

Remove Damaged Slates: Slide a slate ripper under the broken slate to cut the nails holding it in place. Be careful not to damage adjacent slates.
Prepare Replacement Slates: New slates should match the existing ones in size, thickness, and color. If you can’t find an exact match, consider salvaging slates from another part of the roof.
Install the Replacement Slate: Slide the new slate into place and secure it with a copper or stainless steel nail. If nailing is not possible, use a hook or clip to hold it in place.

Inspect Underlayment: While replacing slates, check the underlayment for signs of wear or damage. Replace it if necessary to ensure the roof remains watertight.
Monitor Over Time: After the repair, keep an eye on the roof to ensure no additional slates loosen or shift.

Consult a Specialist: If the damage is extensive or if you’re uncomfortable working at heights, it’s wise to hire a professional roofer who specializes in slate roofs.
Slate roofs can last over a century if properly maintained, so investing in quality repairs is crucial to prolonging their lifespan.