How does cancer spreads via metastasis?

To add to the previous answer:

There are two types of cells - anchored (epithelial), and migratory (mesenchymal).

Anchoring happens by cell-cell and cell-matrix contact. This is achieved by cell adhesion molecules (integrins, cadherins, etc) on the cell surface interacting with each other, and with components of the extracellular matrix (collagen, fibronectin, laminin, etc)

Migratory cells are also seen in many normal scenarios. Bone marrow stem cells must migrate out to form cells of the blood. Cells of a common origin must migrate to different locations in the developing embryo (eg neural crest cells). Cells must also be mobilized to sites of injury to initiate wound closure.

Metastasis happens when cancer cells of a solid tumor 'break free' from an adhesive phenotype and migrate to a different location in the body.

Source:Front. Oncol., 25 March 2014 | http://dx.doi.org/10.3389/fonc.2014.00059

There are numerous signaling mechanisms that play a role in this type of transition of a cancer cell's phenotype. Some of these pathways include TGF-b, FGF, EGF, Wnt, Notch, and even low oxygen.

Much of cancer research is aimed at inhibiting metastasis by targeting these pathways by drugs and gene therapies.