Excellent pics - many thanks! That looks like a Zama (owned by Stihl) C1 series carb......see if you can find the full numbering should you need it again.
Point - Get all of the external crap away before you strip down, you don't want anything going inside!
Pic 1, (L to R) The pump diaphragm which looks like its seen better days! The U shaped flaps are valves that allow fuel to pump - they flap open and closed. On the right is a fine gauze filter that is directly behind the needle valve and allows fuel to it.
Pic 3. That's the needle valve assembly. Removing the philips screw releases the rod that holds the needle....don't lose the fine spring that holds the needle shut!
Pic 4. That's the metering diaphragm controlling fuel from the primer bulb into the carb. It looks reasonable but a bit moth eaten around the circumference.
Please note! Each diaphragm has a gasket with it - when you split them its easy to forget which way round they went so take care.....the diaphragm actually sits onto the alloy carb face in the vast majority of cases.
So....an aerosol of carb cleaner or brake cleaner is essential. Remove every bit of the carb you can and lose nowt
. Squirt the cleaner down each and every orifice both ways. If it gets you in the eye its worth it
Any adjusting screws, count the turns out from fully in.
Replace the diaphragms and gaskets as a set.....genuine Stihl are around £15 but pattern bits are available.
Check out Garden Hire Spares (GHS Ltd) for what you need....sometimes a non genuine carb is cheaper than the genuine gasket set!
Be lucky
John