A cache may satisfy a read from any state except Invalid. An Invalid line must be fetched (to the Shared or Exclusive states) to satisfy a read.
A write may only be performed if the cache line is in the Modified or Exclusive state. If it is in the Shared state, all other cached copies must be invalidated first. This is typically done by a broadcast operation known as Read For Ownership (RFO).
A cache may discard a non-Modified line at any time, changing to the Invalid state. A Modified line must be written back first.
A cache that holds a line in the Modified state must snoop (intercept) all attempted reads (from all of the other caches in the system) of the corresponding main memory location and insert the data that it holds. This is typically done by forcing the read to back off (i.e. retry later), then writing the data to main memory and changing the cache line to the Shared state.
A cache that holds a line in the Shared state must listen for invalidate or read-for-ownership broadcasts from other caches, and discard the line (by moving it into Invalid state) on a match.
A cache that holds a line in the Exclusive state must also snoop all read transactions from all other caches, and move the line to Shared state on a match.
The Modified and Exclusive states are always precise: i.e. they match the true cache line ownership situation in the system. The Shared state may be imprecise: if another cache discards a Shared line, this cache may become the sole owner of that cache line, but it will not be promoted to Exclusive state. Other caches do not broadcast notices when they discard cache lines, and this cache could not use such notifications without maintaining a count of the number of shared copies.
In that sense the Exclusive state is an opportunistic optimization: If the CPU wants to modify a cache line that is in state S, a bus transaction is necessary to invalidate all other cached copies. State E enables modifying a cache line with no bus transaction.