Hi Ed,
It depends a bit on the particular design, but it is usual to start admitting steam just before top dead centre. This can help reduce the load on the bearings as the piston reverses direction, and also means that the valve is more fully open when the steam is really needed, eg as the piston starts to go down the bore.
On the cutoff side, most valve gears are designed to cut the admisssion of steam off part way down the stroke. This allows the steam to expand for the remainder of the stroke. With a simple valve gear the cutoff will be fixed, but the more sophisticated gears allow varying the cutoff. So for instance on a locomotive, for starting the cutoff will be late in the stroke, allowing full boiler pressure on the piston for almost the full stroke. This gives the maximum torque, at the expense of using a lot of steam. When the exhaust opens a cylinder full of steam at full boiler pressure will go to waste. Once the train is rolling the steam will be cutoff much earlier in the stroke, This reduces the torque a bit, but gives much more economical use of steam.
On the exhaust side the valve is usually open for most of the stroke, but in some cases the gear is designed to close the valve as little before top dead centre, with the idea that the compression will help cushion the piston as it reaches the top.
There are some special cases, for instance winch engines and steering engines for ships were usually designed to admit steam for the whole stroke and similarly to exhaust for the whole stroke. This is partly in aid of giving good starting in any position, and partly because such engines never run very fast or for very long, so the extra economy of a short cutoff is not needed.
Another different arrangement is the uniflow engine. These have a valve for admission and a set of ports like a two stroke engine for exhaust. Steam is only admitted for a very short period, maybe 10% of the stroke. The exhaust is only open when the port is uncovered so for most of the return stroke the steam in the cylinder is being compressed. This gives very good economy but such an engine will not self start well unless it is in the right place. They were popular for stationary engines driving mills and factories.
John