Surgeons are guided by imaging devices like PET, CT and MRI scanners. You can use contrast agents to show areas of greater glucose metabolism, for instance, as cancer cells use energy faster than others for respiration and blood vessel construction, and draw a contour around that to be used in surgery and radiotherapy.

Physician here. As others have said, Usually through scans and different tools but visually, youre right, its often a "lump" the architecture of tumours are almost always off from normal tissue. Its just rapidly dividing cells going any which way so more often its just a lump. There is often tumour spreading away from that lump too which is harder to see so they cant just go by that of course.

A common skin cancer is melanoma, and those are made specifically from the pigment producing cells in the skin, so they would be hyper pigmented and often dark. Squamous cell and basal cell skin cancers can be any colour really.

They don't actually look like normal cells. Benign tumors do. Cancerous tumors, while still the same color as the tissue they originated from, usually exhibit a bunch of characteristics that are easy to see on a sample under a microscope. That's why biopsies are a common part of cancer diagnosis. After a surgery, the removed tumors borders are examined. There should be healthy cells on all edges to ensure the entire cancerous mass was removed. This might even be done before the patient is closed back up! Cancer cells are a variety of sizes and shapes rather than uniform; they are immature, often looking like cells from an embryo rather than a person who has been born; they lose their specialized features that allow them to do whatever their function is; they have multiple large nuclei (the part of the cell that holds DNA,) and that DNA is tangled; they contain less fluid; they have more blood supply growing, and they aren't attached properly to each other or surrounding tissues.

And skin cancer might appear darker because your skin is made of different types of cells. If the pigment producing cell (melanocyte, the cell that gives your skin it's color) is the cancerous one, you get a bunch of pigmented cells clustered together and it's darker than the surrounding skin cells that don't make pigment.

not a surgeon/medical provider

From what I've heard, a tumor looks/feels different from normal tissue. Dr. Sandra Lee (aka Dr Pimple Popper) has a few videos on lipomas (a non-cancerous tumor) and I believe at least one has an explanation.

I don't know the answer to your question regarding skin cancers, with the exception of melanoma, which is a cancer of the pigment-producing cells in your skin. This makes it very easy to differentiate on lighter-skinned folks as it is physically darker than the surrounding normal skin.

Cancer cells often do look different than the originating tissue, and can have distinct histologic markers on the microscope.