Combustion

Definition:
Combustion is the sequence of exothermic chemical reaction between a fuel and an oxidant associate with by the production of heat and conversion of chemical species.

A simple example of combustion of hydrogen and oxygen, which is usually used in rocket engines:
2 H2 + O2 → 2 H2O(g) + heat
The eventuality is water vapor.

Double - replacement

Definition: A double replacement reaction is a chemical reaction where two reactant ionic compounds exchange ions to form two new product compounds with the same ions.

Double replacement reactions take the form:A+B- + C+D- → A+D- + C+B-

Examples:
The reaction

AgNO3 + NaCl → AgCl + NaNO3

is a double replacement reaction.

The silver traded its nitrite ion for the sodium's chloride ion.

Single-replacement

A single-replacement reaction is a type of oxidation-reduction chemical reaction when an element or ion moves out of one compound and into another. (One element is replaced by another in a compound.) This is usually written as
A + BX → AX + B
This will occur if A is more reactive than B. You can refer to the reactivity series to be sure of this.

A and B must be either:

• Different metals (hydrogen's behavior as a cation renders it as a metal here), in which case X represents an anion; or
  
• Halogens, in which case X represents a cation.

A single-replacement reaction example:

Fe + CuSO4 = Cu + FeSO4

http://en.wikipedia.org/wiki/Single_displacement_reaction

Decomposition

Discomposition is the process in which an atom is knocked out of its position in a crystal lattice by direct nuclear impact, as by fast neutrons or by fast ions that have been previously knocked out of their lattice positions.

Synthesis

In general, the word synthesis refers to the forming or building of a more complex substance or compound from elements or simpler compounds. For an example in chemistry, a synthesis reaction can be quite simple, like the one below here.
2H2 (g) + O2 (g) -> 2H2O (l)

Another example is like when you write an essay or a poem.