Firstly I must state that when I talk about cancer I am referring to cancers of epithelial origin (eg skin cancer/breast cancer) which make up the majority of cancers. Other cancers such as lymphomas have completely different origins and mechanisms.
Tumour cells will start to release certain proteins called pro-angiogenic factors (such as vascular endothelial growth factor) which diffuse out from the tumour, through the layers of healthy epithelial cells and extracellular matrix, until they reach the cells that make up the blood vessels. The factors stimulate these blood vessel cells to start forming new blood vessels in and around the tumour mass. They are attracted to the growth factors.
As for tumour microenvironment toxicity, one of the major issues is that oxygen is rapidly depleted by the rapidly dividing cells making areas of the tumour anoxic, which is highly toxic to most cells. Epithelial cells are never meant to free from their tissue, where they are layed out in compacted layers and bound to each other and the basement membrane. Having grown away from their originating site, or atleast on top of eachother, they no longer are receiving the necessary signals to stay alive as epithelial cells (not necessarily toxic but would mean death for non-cancerous cells). Lots of tumour cells that aren't able to survive may die by necrosis, where they explode, freeing many harmful internal molecules. I'm prob missing a few things but hopefully you get the picture.
Here is a good introductory online course on cancer that you can take for free (free = no cert and no examination).