The main ingredient of any soup is the liquid. There are a range of stocks that can be used and different chefs are advocated of different types. I'm sure you'll have a favourite but vegetable, chicken and ham stock all work well within a pea soup. Some of you will choose to add just water, preferring the taste of the peas, without the additional stock flavouring.
The next major ingredient is a thickener. Again, there is some variation and everyone will have their own preference but some of the most popular options include whipping cream, double cream and creme fraiche. After stirring it in, you can also add a little extra on top, if you want a thicker consistency. The more cream you add then the thicker your soup will be. If you've not tried creme fraiche before, try it next time you make pea soup. I think you'll be pleasantly surprised.
Finally comes the herbs and other vegetables. If you want to make your soup a little bit sweeter then shallots go perfectly with the peas. Mint and spring onions are also popular additions.