There are 2 methods you could make tea the Indian way.
1) Boil water - nothing is added till the water is boiling. Stop the heat source. Add tea leaves and spices (I will give you a list of spices at the end). The tea and spices are usually added to the boiling water in a Bone China tea decanter. The decanter is then covered with a "tea cozy" for around 3-5 minutes (to allow the tea to brew). Filter into tea cups, add milk and sweetener to taste. This is considered the sophisticated method and is used for the more exotic tea leaves. Usually not many spices are added in this type of preparation. By exotic I would say - Darjeeling varieties.
2) Boil a mixture of water, milk (as much as needed for the entire serving). This mixture is then brought to a boil. Once that happens, add the tea leaves and spices and continue to heat - please note that this is the important difference in the two methods - the "hotch potch" is boiled for about 5 minutes and you would have to keep stirring the mixture (other wise it would boil over). Strain the tea directly into tea cups. This method is used for the not so exotic variety of tea leaves - Basically, you depend on the spices to give you the flavor.
There are a lot of varieties which are used. Combinations are made usually depending on the taste the individual likes.
Ginger (as you had mentioned)
I can give you certain other names - but I know only the Indian names. Don't know the English equivalent. If you are interested you could email me for an extended list. Most of these would be available at Indian (Asian Indian) stores. I am not giving the list right now - by the time you get back to me I'll try and find the English name equivalents.
All these are part of mix-nmatch variety. All of them need to be ground before added to the tea preparation. A coarse grind should be enough. You need not add all, then again you could - depends whether you like what you gat as end product. Trial would help you out.
My favorite though is a mixture of ginger and Cardamom added to tea.
For this I add about piece of ginger (size of a grape) cut in small pieces and 2-3 pods of Cardamom (grind it coarsely - or just powder it with something heavy). This is added for a 2 cup serving.