Communication between cells occurs on a wide variety of levels, from biological hormone transfer to electrical impulses transmitted between nerves. The term for direct communication between cells is Intercellular Communication, or Cell Signaling.
There is no single common method of communication; differentiated cells need different methods, and even more for communication with cells far away. The three basic methods are: juxtacrine signaling for direct contact; paracrine signaling for short distances; and endocrine signaling for long distances (Wikipedia).
When cells can touch, they can release chemicals such as protein which may pass through or affect the cell membrane, or they can form Gap Junctions, a passage directly connecting through the membrane to transmit chemicals. These connections are usually temporary.
For cells further apart, transfer of physical molecules is hard because of the distance, the degradation of the molecules, and the chance of the molecules being absorbed into other cells before reaching their target. Clotting and histamine reactions are examples, as is neurotransmitter function.
Endocrine signaling is the transfer of hormones throughout the body via the Endocrine System, quickly and efficiently sending hormones to localized areas of the body through the bloodstream. This is the way many reactions are communicated, since many areas receiving and sending information are far apart. Endocrine signaling is probably the most common form of intercellular transfer simply because it is the largest method in the body; the others are dependent on local factors.