Although the plaster is missing from the photograph below you can see how difficult it can be to effect a repair in a lath and plaster wall. There are two ways of making this repair and you will have to cut back laths and plaster to the nearest studs either side of the hole to make the repair.
Once you have cut back, you can either place plasterboard in the hole and fix it with galvanised plasterboard nails as shown below. Nails and other fixings can be found by clicking on the link. You may like to take the opportunity to use the hole for providing a place to provide fixings to your lath and plaster wall. Follow the link to find out how.
The gaps around the edges (shown in red) can be filled with polyfiller, one coat plaster or flexible filler depending on their size. Once they are filled the surface can be plastered with skim plaster. You will need to coat the new plasterboard and the edges of the existing plaster with PVA adhesive. Skim plaster goes hard very quickly and even more quickly when its applied to a very porous surface such as the old plaster. Coating with PVA will remove this porosity and make your life much easier.
Or you can buy some galvanised mesh called Expanded Metal Lathing, or EML for short and simply nail this between the studs, keeping it a tight as possible and plastering over the top. This is the method preferred, and used by most conservation and heritage groups as it keeps the integrity of the wall and allows for the same, slightly uneven finish, associated with lathe and plaster walls. The EML and all associated tools are shown below. Simply click on them to buy. EML needs to be cut using tin snips and can be cut to the shape of the hole and can be easily fixed with galvanised staples. The roll of EML is 60mm wide and ideal for small repairs as it can be applied in rows. More than 2 rows will almost always need reinforcing with extra noggins. The mesh can be used for larger repairs or even new walls. Using ordinary staples and/or nails can lead to rust developing which will show through to the surface very quickly and probably spoil any decoration you have applied.
If there is too much slack in the EML repair then it may be easier to insert a new timber noggin to give the repair greater strength. The noggins are inserted easily by cutting a length of timber to fit between the studs and screwing at an angle into them.
Finally apply your plaster. This can be done by applying a suitable base coat plaster and then a skim layer on the top. For base coat plaster it will be best to talk to your local builders merchants as there are quite a few plaster varieties about these days. Make sure you tell them that the plaster is to be applied to EML. For smaller repairs there is a One Coat Plaster available, which is called Universal One Coat Plaster but in DIY stores generally comes in smaller bags than the 25kg usually available from any builders merchants. This sometimes called Patching Plaster.