Hora, it really it pish easy.
Rake out existing mortar to a depth of no less than 15mm, brush out dust and loose material. Then dampen before replacing the mortar.
I’d use a 5 to 1 mix (sand/cement), on brickwork or a lime mortar on stonework. Mix to a firm consistency, not to wet else it’ll stain the wall easily. Use a plasticiser additive to help keep the mortar workable.
Various finishes can be used, weather struck is best for areas well exposed to rain. Bucket handle(half round) for general use. For stone,ragged or cut joints look best. All finishes look best brushed once firmed up nicely.
When are you thinking of getting it done, i’m needing to raise some cash so would be interested in doing it for you.
Sharki.