A conservator can tell if a painting needs cleaning or needs conservation just by looking but knowing if it is safely cleanable is a different story. Tests must be run and most all conservators will charge you for this testing procedure and the exam that goes along with it. The information is valuable and takes time, like a complete physical exam at a doctor's office. Oxidized yellow varnishes are not always safely removable. Some antique resins are completely insoluble and impossible to remove, others are not true artist's varnishes.
All paintings clean differently.
Various soaps are used to remove grime,dirt, grease, and nicotine layers. Various solvent solutions are used to carefully remove and reduce oxidized varnish layers and the conservator tries to go down layer by layer. If the original varnish is intact and unstained underneath all the added layers that is a bonus and it can be left in place. There are always some exceptions but usually, after cleaning, the painting is revarnished to protect the surface. Conservators do not have to apply a final varnish however it will leave the painting unprotected and most likely shorten the painting's life.