Best method to cure cancer as of now?
There is no general therapy for cancer - as there is no general cancer. Cancer is the umbrella term for a disease where you have body cells growing without control, leading eventually to death. But since there is a wide variety of cells in the body, there is also a very wide variety of different cancers.

To treat these, surgery is often the first line of therapy. For some cancers this is already sufficient to cure the patient, examples are skin cancers (not only melanoma but the other forms as well) where you can cure a very high potion of the patients. This only works for early forms of the cancers when there are no metatases present.

Besides this, additional therapies are used - as you said yourself chemotherapy in the different forms as well as radiation therapy. Chemotherapy is given systemically and targets fast growing cells (cancer cells have these properties) and causes mutations or other problems which let the cancer cells eventually die. Radiation works with the same principle, but is more focussed.

Relatively new therapies are the targeted therapies where the treatment uses the occurance of certain common mutations. An example would be the mutated BRAF kinase in melanoma (and also in a number of other cancers) which can be specifically inhibited with an inhibitor. This avoids a lot of problems general adverse effects of the drugs. Additionally immune therapies are also new which use antibodies against surface receptors of T cells to prevent their inactivation. These T cells then attack the tumor.

These are all non-biological treatments. More biological ones are modified oncolytic viruses. In this therapy you inject genetically modified viruses which preferrably infect the tumor and then destroy it. These are relatively new, but an interesting option. See references 1 and 2.

An old method is the usage of bacteria to treat tumors - the first obervations on this where done in the late 19th century, see reference 3 for more information and a lot of further references.

A number of the chemotherapeutic drugs used today are originated from nature, but are today synthesized and used in a pure form and not isolated from their origin anymore. Examples would be vincristine, irinotecan, etoposide, and paclitaxel. See references 4 and 5 for details.

Besides this, there are no effective "natural" cancer cures, despite the claims of several "alternative medicine people". These are either based on wrong assumptions of biology or wrong ideas like Homeopathy.

References:


Advertisement Oncolytic Viruses and Their Application to Cancer
Immunotherapy
Oncolytic viruses: a new class of immunotherapy drugs
Strategies using bacteria to target tumors
Anti-inflammatory and anticancer drugs from nature.
Drugs From Nature, Then and Now