Usually, I help myself with cream and sugar when I was ordering coffee in my university's cafe. But I was really confused what unit should I use to describe the amount that I need when I am asked.
When I'm being served coffee by a business, like at a cafe or on a plane by a flight attendant, the assumption is that they have some prepackaged amount available, so I just respond with the number of packets I would like.
For example, "One sugar and two cream, please." or "Just one sugar, please."
If someone is serving me coffee and the sugar and cream aren't likely to be prepackaged, like at a friend's home, I will explain sugar by spoonfuls, and cream by a splash/a little/a lot and suffer silently when it isn't quite how I would make it :)
Usually if my friend doesn't know how I take my coffee, they bring the sugar bowl and cream pot and let me add the cream or sugar myself.
This borders on a lecture on the Imperial measurement system rather than the English language, if you want to make sure you get the right amount. I believe cream and sugar packets are distributed either by the teaspoon or tablespoon-ful. Consult the packaging next time you see one. Most native speakers have the same issue you do, which is why most modern coffee shops have a small bar to allow you to add cream and sugar yourself. Also, even many Americans and British citizens hate using the Imperial system, especially for volume.