1. To do something thoroughly is to do it well, and miss nothing. It implies a lot of effort to ensure the job is done.
He washed the jug thoroughly. He soaked it, then he scrubbed it, then he rinsed it, dried it, and checked to make sure it was clean.
2. To do something completely simply means 100 percent.
The jug is completely full. There is no room to add any more.
3. Exactly means that whatever it is describing is accurate or precise.
The jug holds exactly one litre. He uses it to measure the ingredients because it needs to be accurate.