Acetylcholine and Dopamine: neurotransmitters involved in dreaming
Dreaming is suggested a result of several mechanisms - certain brain wave and brain region activations, as well as, to an extent, neurochemicals such as neurotransmitters.
Theories suggest that dopamine plays a strong role in dreaming. Research has shown that dreaming can be manipulated by dopamine agonists (that stimulate dopaminergic receptors), and through forebrain stimulation (which is dopaminergic - i.e, transmits dopamine). Moreover, forebrain lesions, likely dopaminergic, inhibited dreaming.
Dopamine is produced by dopaminergic neurons within the dopaminergic pathway - including the substantia nigra, ventral tegmental area, and hypothalamus.
Here, tyrosine is converted to L-DOPA by the enzyme tyrosine hydroxylase (TH). This, in fact, is also used to make epinephrine (see below).
Evidence has also indicated that cholinergic receptors (i.e, they respond to the neurotransmitter acetylcholine) contribute to dreams. Specifically, introduction of cholinergic agonists (i.e, molecules that stimulate the acetylcholine receptors) induced dream reports.
Again, acetylcholine is produced by cholinergic neurons in the cholinergic pathway. 
Chemically, acetylcholine is produced from choline via the enzyme ChAT (choline acetyltransferase).
Dreaming has also been linked to lower levels of serotonin. It has also been suggested be due to lowered histamine, and norepinephrine. However, as you have not asked for the absent neurotransmitters, I will not delve into this further.
Just to further briefly describe existing knowledge on how dreams occur: dreaming is known to correlate with Rapid-Eye-Movement (REM) sleep, but has also shown to occur in non-REM sleep. Research has also found decreased activity in posterior cortical regions, increased limbic activity (mediates emotion), while dreaming. Dreaming has also been associated with the parietal and occipital lobes of the brain.
A summary of brain regions more activated and less activated, during REM and NREM sleep respectively, is below.