To my knowledge, it depends on the solvent used especially if it is an organic solvent you can have inverted micelles. To determine if you have micelles or not, you can determine the critical micellar concentration (CMC). Beyond this value, you have micelles formation in the solution. To do it, you can simply calculate the surface tension according to surfactant concentration whatever the method (pending drop technique for exemple). The surface tension will decrease according to the surfactant concentration and then will reach a plateau.
the solvent polarity is the deciding factor for a surfactant to aggregate in a normal or reverse fashion. mixing polar cosolvents with water will give normal micelles. Non polar or water in oil will give inverted micelles.
Solvents play a crucial role in the structure of micelles whether it is normal or reverse micelle. For determination of CMC, the simplest technique would be conductivity measurement.
The formation of a micelle or of a reverse micelle depends on the media, and in the case of reverse micelles on the presence of water in the organic solvents. The polarity of the solvent determines which part of the surfactant is "exposed" to the solvent and which one is "hidden" to the media. In the case of water the micelle is formed in order to "hide" the hydrophobic portion to the water, in the case of organic solvents a small amount of water (even the small percent present in each organic solvent) is needed to form a reverse micelle, and also a "water pool". In water solution conductivity is the easiest way to determine micelle formation, in organic solvents the micelles formation determination is a little bit harder: NMR, light scattering or other spectroscopic measures can be helpful.
there is a big impact of geometry of surfactant, i.e. ratio of area of polar to apolar part of the molecule. Large polar group favours 'normal' micelles, if the opposite is true reverse micelles are favoured, simply because there is a good fit with the spacial requirement inside the micelle, which is very different for micelles and reverse micelles.
I've seen most of the attention on the solvent (except Titus Sobisch, who referred, and well, the surfactant geometry). In fact, solvent is important, but what is most important is the spontaneous curvature of the surfactant, or in other words, the geometry of the surfactant. It is the curvature/geometry of the surfactant who will determine if the surfactant film “curves” towards oil (forming normal micelles, dispersed in water), or curves towards water (forming reverse micelles, dispersed in oil).
Assuming what you are interested are real micelles, and not emulsions (which are thermodynamic unstable):
For instance, you may have an oily solvent, but if you had SDS, which has positive curvature, you will not form reverse micelles, because SDS does not curve into oil.
You may be able to change the curvature of SDS though (this can be done by adding a co-surfactant like a long-chain alcohol). If you manage to change the curvature to negative, then you might be able to form reverse micelles.
Perhaps the most well-known example are non-ionic surfactants such as C12E5. These surfactants change their curvature as a function of temperature. At room temperature, they have positive curvature, and they want to form normal micelles. At high temperature they have negative curvature and want to form reverse micelles. If you have a mixture of water and oil (say, decane), just by increasing the temperature, you will shift from normal to reverse micelles. At intermediate temperatures, you may form bicontinuous micelles.
Search in the literature the work from Strey and Olsson, and the “Phish” diagram for nonionic surfactants to learn more on this. For instance: