Welcome to the wonderful world of DIY where even the simplest question often has a complicated answer!
You really need to know how your house is constructed, it can save lots of aggro if you do. You say it’s a solid plaster wall so I assume it is brick or block work about ½ inch under the surface.
There will be a hidden lintel above the window supporting the house structure above, about 6 inches deep and extending about 4 inches past the window on either side.
What it is made of will determine how easy the job is, it will be wood in older
Victorian style properties and perhaps still used as late as the 1930’s Concrete or steel in later ones.
If its wood a masonry drill through the plaster and then just put a screw into the wood job done!
Steel and concrete are difficult, with concrete unless you have an SDS drill you will be there all day trying to drill a hole and frankly my purely personal view is I prefer not to drill into them for fear of causing cracking. Steel should also be avoided unless you are experienced and sure it will not cause problems.
The best way is to buy a blind wider than the window, that you can fix to the brick either side of the lintel, or fit a wooden batten to the wall fixed securely 6 to 8 inches or so either side of the window in the brick and with a bit of no nails on the back for good measure and paint it to match the wall. You can then fit your blind and any later poles etc to the timber in a jiffy with wood screws.
Drilling brick is simple just use a masonry drill to the depth (a hammer drill is a must) you need to push a wall plug in (they are marked what drill size they require) and screw into that, always aim to get at least 1 to 1 ½ inches of screw into the brick, the plaster has no strength to hold a blind. Always look out for any signs a cable or pipe might be buried before drilling walls, as a rule though it would be very unusual to find either around a window.
Treat yourself to a pipe / cable locator if you are going to be doing lots of DIY it could save a lot of grief later!
Sorry to drone on, but tried to cover the main points hope it hasn’t scared you off! If you get stuck just say there’s lots of helpful people on here who can advise.