For repointing, you will need:
The usual mix is a 6:1:1 mix of sand/lime/cement or 3:1 mix of sand/lime. Use sharp sand with lime, and soft sand with cement.
To colour the mortar, either use a stain, or replace some of the sand with ground up bricks. Black mortar is coloured with ash. An organic stain is best as it will weather. Other recipes are in the Materials section. A bit of trial and error will be needed; make two or three measured samples, add water, allow them to dry. And then pick the best recipe.
To make up a sample, use a yoghurt carton to measure the proportions, mixing the sample in a bucket. Record the proportions and materials used. Tip the mix out on to a sheet of plywood or a spot board. Do not touch it with a trowel, otherwise you will bring water to the surface and this will carry the cement and lime and alter the colour. As you tip the mix out, smaller 'crumbs' will fall to the side. Heat these with a hot air gun and they will dry out very quickly. Pick up a dry crumb and compare with the mortar you are trying to match.
If you need to fill cracks and joints between wood and stone, wood and brick, or stone and brick, avoid putty or modern fillers. Instead use either lime putty or a mix of non-hydraulic lime, ground chalk and water.
If you need to re-point an old wall (pre-1900) then you should be using a lime mortar. Old bricks and many stones are soft and the use of cement mortars will eventually destroy the structure of the wall.
Damp down the brickwork and the mortar joints - it is very important that the wall is damp. That may mean spraying, for example with a plant sprayer, and letting it soak in for a few hours. If your wall is very dry it is wise to spray it the day before as well. This helps to prevent the mortar from drying too quickly, helping it to bond better without cracking.
Knock up your mortar. If you've got pre-mixed lime coarse stuff (1 part lime putty to 3 parts well graded sharp sand) then remove any excess water on top of the mortar and tip the mortar out onto a wooden board (allowing any excess water to soak away). Knock up the mortar well to make it workable. Lime mortar is a thixatropic material - the more you work it, the softer and wetter it becomes. So even if it feels fairly dry and stiff to begin with, persevere and only when you find yourself getting really tired should you add a small amount of extra water. Too much water in the mortar increases natural shrinkage and can lead to cracking. If you want to mix your own mortar use the mix ratio above - a specialist supplier will help you buy the right materials.
Put a small amount of mortar on your hawk and, using your trowel or pointing iron, work it down into a pattie approximately as tall as your mortar joints. Chop the edge off the pattie with your trowel/pointing iron. The mortar should be of a consistency so that about 2.5cm (1 inch) stands off your trowel easily. Always work towards your previous (or original) mortar, pushing the mortar firmly in place. Use a narrow pointing iron and try to keep the mortar off the face of the bricks - any overspill (or feathers) are best left until leathery hard. Avoid over-working the face of the mortar once it's in the wall as this may make it whiter and weaker.
Apply the mortar in layers, pressing it into the joints. Pack the head (vertical) joints first and the bed (horizontal) joints second. Use the jointer to make straight, even bed joints. Match the mortar finish to that of any original joints, typically slightly depressed; fill the joint flush and then use the jointer to leave a shallow groove. Make sure you finish the joints before the mortar gets too hard.
After three to four (depending on weather/temperature), the face of the mortar should be sufficiently stiff so that you cannot mark it with your thumb but you can with your nail. Take a piece of wood that has been cut off to an angle of approximately 45º and is about the same width as the joint. Run this along the joint, applying constant pressure. Most of the feathers will drop off. If you're working during the colder months, it will be necessary to cover the mortar with hessian (and maybe polythene) to prevent it being damaged by frost attack. It's also advisable to cover mortar (with damp hessian) on hot or windy days as these elements can dry it too quickly - leading to cracking and weak mortar.
Use a stiff brush to brush off the remaining feathers and then stipple/tamp the surface of the mortar joints to reveal some of the larger aggregate and simulate some early weathering.