What type of lens hood do I need?

I have a micro nikkor 105 mm f2.8 lens but no hood, I asked in the local shop and they did not know, the filter size is 52 mm

You need a screw hood 52 mm

You want the Nikon HB38 lens hood.

The two requirements are:
1.it must screw into the 52mm ring on the front of the lens.
2. The depth of the hood must be as deep as possible without vignetting at the maximum aperture setting.

The HB38 is designed specifically for that lens. You may be able to find an aftermarket hood that is less expensive - Nikon charges premium prices for lens hoods.

You need to find a lens hood that fits your cameras focal length

Too long and it will vignette you images, too short and it will not do well at preventing ghosting or lens flare.

Nikon does not make a lens hood for that manual focus lens.

The AF-S 105 mm f/2.8 lens does have an available lens hood that fits its 62 mm lens filter thread

Nikon's old 105 mm f/2.5 lens (not macro) had a 52 mm lens hood available. Finding one may be problematic, but that is the hood you will want to research