Proficiency bonus is based on the Level of a character and nothing else; class or race don't matter, only the level of your character. For every skill you are proficient in you get the following bonus based on the level of your character: (Basic Rules, p. 10, Character Advancement Table)
Level / Proficiency Bonus
Each Class has a "Proficiency Bonus" chart under that class in "Chapter 3: Classes" in the Players Handbook (PHB). For some classes the chart is a stand-alone chart, like the fighter's on page 71. For the Druid the proficiency chart is part of the spell chart on page 65. All the classes have the exact same proficiency bonus chart so you can look at any class to determine your proficiency bonus. If you make a check on a specific skill you are proficient in, a weapon you are proficient in, or a spell you get both your standard modifier for that ability AND your proficiency bonus.
The proficiency bonus is also used to determine saving throws (DC) against any spell you cast. DC to resist one of your spells equals 8 + your spellcasting ability modifier (INT, WIS, etc.) + your proficiency bonus + any special modifiers. There are more particulars, but these are the basics and all you need to know to get started.
It took me a while to figure this out when I started playing and I think once players get it down it is very simple and they forget how complicated it can be for beginners. The PHB really does not lay this out very clearly; the necessary information is spread out over 3 or 4 chapters when it could be simply stated in one or two paragraphs and a single chart.
I hope this helps you.