The method proposed here is mostly in use for higher Diptera, but I don't see a reason why not to apply it to the lower ones, too. In principle haemolymph and the internal soft parts are transformed by KOH into a sort of soap, which is washed out by glacial acetic acid. Dissection, inspection, and photography are done in glycerol. One advantage of this method is, that no poisonous substances are involved.

The chemicals needed are: 10% KOH, pure water, glacial acetic acid (99%), 2-propanol, glycerol. They should be available in your local pharmacy.

To be able to work without a coverslip in glycerol, check the working distance of the objectives of your microscope. It should be at least 2mm. The usual objectives with 20x and 40x magnification have a far smaller working distance and you'll have to buy objectives from an inverse microscope. If you plan to buy a new microscope, the minimum requirement should be, that such objectives are available.

Furthermore I use a set of watch glasses, Dumont forceps, dissection pins, and an acute scalpel.

Detailed Recipe:

1. Make a photo of the whole specimen to show colour, size ratio, and dusting.
2. Remove the terminalia with Dumont forceps and an acute scalpel. For fresh and alcohol material, hold the fifth segment with the forceps from the side and cut between fourth and fifth segment. For some groups like Agromyzidae, where the phallapodeme fills the whole abdominal cavity, and all dried material, remove the whole abdomen (break it off).
3. Leave the terminalia in 10% KOH in a "covered watchglass" overnight. Boiling for 5 minutes has the same effect.
4. Possibly transfer it to pure water. This is necessary for legs or the head, because they can break by the CO2 bubbles forming in the next step.
5. Transfer it to glacial acetic acid for ~10 minutes.
6. Possibly transfer it to 2-propanol, if too many gas bubbles cover the delicate parts.
7. Transfer it to glycerol and wait until no more streaks are visible on moving it around.
8. If the object is too large, start dissection in a watchglass and make the first photos under the binocular.
9. Transfer the part(s) to a drop of glycerol on a slide with a rounded cavity. The drop size should be 1/3 of the cavity's diameter.
10. Dissect and orient under the binocular and inspect and make photos under the compound microscope.
    

Some comments:

Point 3: "Overnight" is just a typical time, for Chironomidae an hour can be enough, Bibionidae I'd usually clear, dissect, and clear again. From the other two clearing chemicals I've seen, I found lactic acid comparable, but didn't check it thoroughly (try it), and Kreosote is carcinogenous. For using Euparal see below.

Points 7-10: The most important reason for bad resolution in glycerol is, that one doesn't wait long enough for homogenization. A typical value is 1 hour, but for large parts it can be much longer. And you have possibly to wait again after every dissection step. Bear in mind, that even if you don't see any streaks under the comparably low resolution of the binocular, they can still be strong enough to degrade the image in a compound microscope. The second reason is, that the parts are floating around, or, if you want to show a part in an upright orientation, slowly topple over. This movement is mostly too slow to be observable under the binocular, but in a series of exposures to be used for focus stacking, it is clearly visible. Mostly this oblique stack can be corrected in the same way as the stack resulting from a binocular. Here is an example.

The highly diverse structures of the terminalia among Diptera makes it impossible to give a unified howto of dissection. The first two examples below show the typical brachyceran condition consisting of epandrium, hypandrium and appendages. The next two show the typical nematoceran forceps type. And finally I show two examples of the many groups, which differ from the two basic patterns.

Dissection Examples:

1. Suillia fuscicornis
2. Helina latitarsis
3. Trichocera saltator
4. Mycetophila uninotata
5. Megaselia variana
6. Simulium angustipes
   

The last point to mention is permanent embedding of parts on a slide to be able to use objectives with a higher resolution. In some groups like Chironimidae, Phoridae, Sciaridae, specimens are embedded immediately, even before inspection. In other groups, mostly calytrate flies, the experts avoid embedding at all. Thus, at first sight it looks like embedding is appropriate in some groups and inappropriate in others. But obviously embedding has the same advantages and disadvantages in all groups. If you embed, you might miss characters, because after the sample is dried, the side view of the parts is lost. If you don't embed, you might miss characters, because some of them only become visible at higher resolution in the embedding. Below I try to show a way through this dilemma by discussing some pros and cons, present different embedding media (and methods), and show some comparisons between exposures taken in glycerol and Malinol (artificial Canada Balsam, chemically identical.

But first let me continue my recipe above for embedding in Malinol:

11. Transfer the dissected parts from glycerol to 2-propanol with Dumont forceps. Very small parts are best lifted out on the flat inner side of the forceps.
    
12. After about 1 hour pick out the larger parts with the forceps, place them on a slide and add a drop of mountant. The more delicate small parts are sucked into the tip of a pipette and placed together with some alcohol on the slide.
13. After ~2 minutes the alcohol has disappeared and the parts stop moving. Orient the part with dissection pins and place a coverslip on top, which is pressed down under the binocular, such, that the orientation is preserved.
14. Make the first image at high resolution.
    
15. After a few days the mountant has sufficient viscosity and we can start to reorient the parts, by moving the coverslip and by exerting a slight pressure on one side. This way we can show the parts in different orientations.
    

Some comments:

Point 12: Take care that the alcohol doesn't evaporate befor you've added the mountant. This causes irreversible damage. Sometimes I place an extra drop of alcohol on the slide, before I transfer the part (e.g. for legs). As Malinol is strongly adhering to all materials, I found it convenient to use tooth pickers to control the drop size and to discard them immediately into a closed bin. The small drop remaining on the pin after orienting the part, I remove with soft toilet paper.

Point 15: At this point we'll notice that drop size is crucial. As Malinol almost doesn't shrink, it is less risky that a too small drop causes distortion of the parts. But a too large drop can cause a very slow reorientation, and after a few days you must correct it. Even worse, too large drops make the use of objectives with higher resolution impossible, since Malinol has the same refraction index as glass and high resolution objectives are calculated for standard coverslips with 0.13-0.17 mm thickness. The best resolution can be achived, if the amount of mountant is just as large as necessary, but this might prevent us from showing different orientations. If you want to reorient the parts, don't use too small coverslips.

Please note, that for embedding in Malinol no poisonous chemicals are needed. Xylene only comes into play, when we have to redissolve a slide, see below.

The usual alternative to storing the dissection result on a slide is to store them in "genitalia vials" in glycerol. A clever alternative is to glue the parts on a piece of card and attach it to the same pin as the fly (recipe from Michael Ackland). Bear these methods in mind for the following pros and cons of embedding.

Against embedding:

• Slide and fly can get separated.
• After drying only two views are left, from above and below.
• Sometimes the higher resolution is of no taxonomic use.
• Redissolving a Malinol slide is tedious and difficult without a proper chemical lab.
  

Pro embedding:

• With slides we get the best resolution.
• It is much easier to compare, say, 10 slides, than to soak and put back to glycerol the contents of 10 microvials or ten pieces of card.
• Redissolving is always possible without damage.

Comparison of Embedding Media:

DMHF (Dimethyl Hydantoin Formaldehyde):
Mostly used in the UK. Can be soaked in water in a few minutes, the other media need about a day. The surface hardens quickly, which makes orientation inconvenient.

Euparal:
Mostly useful to embed undissected material (terminalia of Chironomidae or Sciaridae), because you save the clearing step. The sample takes days - weeks until complete clearing is achieved. I stopped using it after I had trouble with redissolving, but this might have had different reasons. You should definitely try it.

Malinol (artificial Canada Balsam, chemically identical):
Only one disadvantage, it can only be redissolved in xylene (probably even better in benzene, but this is even more carcinogenous). Xylene shouldn't be used outside the flue of a chemical lab, especially not in living space. If you really have to redissolve a Malinol slide, here is short description. The two important advantages of Malinol are, that it is not shrinking (there's almost no risk of distortion) and you can show different views in the same embedding (see recipe, point 15)

Finally have a look to some photos of the same object taken in glycerol and Malinol, which should help to make a decision whether to accept the extra work and to take the risk of having to redissolve.