It depends on whether it's local flora or alien taxa. I suppose you mean unexpected plant for your area, which you don't have any idea about it.
In this case, a good starting point could be to find the genera with google images if we have some idea about the family. We can keep trying with family, flower color, leaf shape, etc. It's very possible to find some suitable genera and their distribution.
Once we have a short list of possibilities, we could search in local floras available in internet, with good and solid information.
You can find two different examples in links below:
efloras.org: with Flora of China, of Chile, of Misouri, of North America, etc.:
http://www.efloras.org
Muestras Neotropicales de Herbario, a visual herbarium of Neotropical countries:
I agree with C. G. Beliver. First thing is to identify the plant on the basis of family.
After knowing the family one can search for the species. For this one can go through the flora of that particular region if available. Sometimes a species have special characteristics related to leaf, flower or fruit. These can also help in the identification. Leaf type and arrangement may also be useful.
After years of developing my own plant identification skills, I have to agree that I first attempt to identify the plant family based upon my own experience and observation. Then I can usually narrow it down to genera and then species with the help of floras, comparing herbarium samples, online resources such as eFlora, or connecting with local experts or others I know to have expertise in the specific family or genera (sometimes professionals, registrars or amateur experts). Monographs are also good references once you know the genus.
Granted most of these techniques rely on basic observation skills and older established plant taxonomy. But there are other references to check the current taxonomy after you have a name for the plant.
I don't think there is one plant genera or family that is particularly difficult. More often it depends upon your own experience with any given group of plants.
I agree with the steps Rhoda has provided. I think getting a handle on the family spotting characteristics of your regions iconic flora (for example) is a really useful first step, especially as an introduction to what becomes such huge variation you see in the wild.
I must say I am looking forward to a phone app which can assist with identification to species level, in the field