Wow, theres a question you shouldn't ask on a forum I use. Prepare to be bored.
Lime mortar is a very good product and wholly appropriate for use in building/repairing/repointing old or new walls. It is widely (and incorrectly) considered to be a pain in the arse to get hold of and store, but any decent builder who knows his marbles will tell you it's a beaut to build with.
If you are repointing an existing wall (which presumably was originally built with lime mortar) then the easiest thing to do is get your hands on a bag or two of Castle Cements Natural Hydraulic Lime (it comes in three types NHL 2, NHL 3 and NHL 5 which relate to the hydraulice setting properties of the mortar - basically don't worry about it and go for the middle one if given the option but any of them will do - NOTE it might be 3.5 not 3 as this is all off the top of my head). If you go to a builders merchants and ask for it they will quite possibly look at you a bit funny, hum for a minute or two then offer you Hydrated Lime ("it's the same stuff mate honest"), don't believe the hype it isn't the same at all. The Castle Cement Hydraulic Lime comes in a 25kg paper bag just like cement.
Right then sourcing this product is the hard bit, using it is a piece of piss. Mix it with some sand (I would suggest a 1:4 or 3 Lime:Sand ratio), then add some water so it is workable. Then get to the repointing. It is worth trying different sands in order to get a good colour match with any existing pointing/the stonework/the missuses favourite deckchair etc etc.
To do the repointing simply scrape out all the loose old stuff to a depth of at least 1cm (but more if need be) then give it a good brush to get rid of loose rubbish. Dampen the gap with water (I use a plant sprayer thing but a sponge or big paint brush would work just as well). To put the mortar in the best technique is to have a hawk (flat thing with a handle underneath it) with some mortar on which you hold up to the gap to be repointed and with a pointing trowel (like a slightly long metal lolly stick with a couple of bends in it and a curved face) scrape some of the mortar into the gap. However theres no real need to buy these tools if you don't have them as a bucket and a small standard (pointed style) trowel will do the job fine. It just might take a bit longer. Make sure you work the mortar well into the gap.
There are various finishes you can go for with your pointing (recessed, cut, flush cut, flush, ribbon) but IMHO the easiest and most universally appropriate is flush. Which is just flush. Avoid ribbon finish like the plague - this is the one that stands pround of the stone/brick work and looks appalling and is (in certain situations) actually detrimental to the walls condition.
Once you've done the pointing leave it for a while (hour or so) then brush it with a stiff brush, then leave it, then brush it repeat until you're happy with the finish (don't brush to much or you'll pull out the mortar you've just placed.
Be aware that lime mortar sets much more slowly than cement based mortars. It will develop a skin hardness over a few hours to a day but can take much longer (a month+) to reach full strength, not that this is really an issue with repointing. Also lime mortar is more sussceptible to frost damage whilst it sets than cement mortars (again not really an issue at this time of year).
The advantages of using lime mortar are:
It's nicer to work with
You can clean off spills more easily and more successfully
It is more 'in keeping' in a traditional building
It is more environmentally friendly
It is more 'flexible' when set so can absorb small amounts of structural movement
It looks nicer
Things to be aware of with lime mortar:
It is nasty stuff to get on your skin or eyes (apparently worse than cement). Having said this I happily throw it around without gloves or goggles and have suffered no ill effects
It sets slowly
It is awkward to get hold of.
It is more expensive
Another couple of options are:
1) You can get lime putty, which you can then add sand to and proceed as above. You need to use this if you're doing fine lime plastering but for repointing the bagged dry stuff will be fine and is just easier, and more familiar if you're used to cement.
2) You can use hydrated lime with cement. Some people (who are wrong) consider this to be lime mortar (I have had architect and engineers tell me that lime mortar has to have cement in it - morons). In reality it is a bit of a halfway house but hydrated lime is easy to get hold of, as is cement. I would suggest a 1:2:6 lime:cement:sand mix if you do this but to be honest it really isn't the same.
3) Just use cement/sand mix 1:4 cement:sand should be fine, but then you would be a bad man
Rough Prices:
25kg Castle Cement Natural Hydraulic Lime - £13
25kg Hydrated Lime - £6
25kg Cement - £4
25kg sand - £2