When tumors grow to a certain size, they will start to develop a "tumor microenvironment", which is a umbrella term for all kinds of cells and tissue beneficial to the tumor, in most cases fibroblasts (cancer-associated fibroblasts) and macrophages (tumor-associated macrophages), but it depends on the specific kind of tumor and its organ.
As tumor cells exhibit a drastically increased metabolism, they will begin to suffer from hypoxia (low oxygen concentration), which is signaled via several different biochemical pathways to the microenvironment and leads toward angiogenesis, the creation of new, often malformed, blood vessels, towards the tumor mass.
The tumor can now increase its mass further due to the continual metabolic supply and the cells can undergo a process called "epithelial-mesenchymal transition", which will allow the tumor cells to "detach" themselves from the primary organ (intravasation), enter the blood system and colonize "pre-metastatic niches" => new tissues and organs.
Some tumors are able to prime distant organs for metastasis via the secretion of specific factors and in many cases tumors show a distinct preference to metastasize in particular organs.
Ralf et al (2007): Molecular regulation of angiogenesis and lymphangiogenesis
Costa-Silva et al (2015): Pancreatic cancer exosomes initiate pre-metastatic niche formation in the liver
Egeblad et al (2010): Tumors as organs: complex tissues that interface with the entire organism
Bu et al (2019): Biological heterogeneity and versatility of cancer-associated fibroblasts in the tumor microenvironment
Jang et al (2019): Integrins, CAFs and Mechanical Forces in the Progression of Cancer