Solar Spectral Types and Dwarf Stars On the following page, 

http://www.uni.edu/morgans/astro/course/Notes/section2/spectraltemps.html

It mentions Main, Giants and SuperGiants.

However for Dwarf Stars (e.g. D, Sd) , do I apply Main Sequence to the solar type?

For other types, IV, II, do I apply Main Sequence / Subgiant / Giant to the type?

If you look at the linked webpage, you'll see it mentions Types (V,III,I) but for instance where would Procyon (F5IV-V), Sargas (F1II) fit or should there be a different table for types IV, II?

Would groups (D, sd, IV,m II) have a different table?  Rigil Kentaurus (G2V) would clear fit into Main Sequence.
The modern system of stellar classification is 2-dimensional, with one axis conveying spectral class, and the other conveying luminosity class. The spectral types are as follows:


O-type, "blue", $\geq 30000$ $\mathrm{K}$
B-type, "blue-white", $10000-30000$ $\mathrm{K}$
A-type, "white", $7500-10000$ $\mathrm{K}$
F-type, "yellow-white", $6000-7500$ $\mathrm{K}$
G-type, "yellow", $5200-6000$ $\mathrm{K}$
K-type, "orange", $3700-5200$ $\mathrm{K}$
M-type, "red", $2400-3700$ $\mathrm{K}$


There are also some extended spectral types, including D for white dwarfs, C for carbon stars, and several more for brown drawfs. The above are the predominant.

The magnitude axis consists of the following groupings:


0-type, "hypergiants"
I-type, "supergiants"
II-type, "bright giants"
III-type, "giants"
IV-type, "subgiants"
V-type, "dwarfs" (these are the main-sequence stars)
VI-type, "subdwarfs"
VII-type, "white dwarfs"


When these systems are used, a spectral class is combined with a number ranging from 0-9 which symbolizes the location between adjacent spectral classes, and the luminosity class is then appended. 

For example, the Sun is a type G2V star. This means it is a G-type star on the main sequence. It could then informally also be referred to as a "yellow dwarf".

The system is more complex than this, and there are many additional suffixes and other symbols to further explain the nuances of individual stars. This does cover the basics quite well, however.