Synthesis reaction: Note if the reaction has only one (complicated) product. If there is a single production with notation "AB" (or ABC, etc...), then you can be sure this is a synthesis reaction. Synthesis reactions are a union of two (or more) reactants (A and B) into one new product (AB). The reaction has form A + B -> AB. Even though entropy decreases---going from two free chemical groups to one---the energy release is enough driving force for many synthesis processes.
Decomposition reaction: Look for a "breakup" to identify decomposition reactions. Decompositions are synthesis-in-reverse. A complicated molecule of form "AB" separates into its constituents. If you see one "complex" molecule breaking up into several simpler ones in form AB -> A + B, you've found a decomposition reaction.
Single-replacement: Remember that single-replacement reactions switch the identity of the simpler, un-bonded group. The general formula for single replacement reactions is: A + BC -> AB + C (or AC + B). Before the reaction, the "A" is by itself, while chemical groups B and C are combined. Single-replacement processes shuffle this order, so that group A bonds to either B or C.
Double-replacement: Keep in mind that double-replacement reactions have products as complicated---in terms of bonded chemical groups---as starting reactants. The process is: AB + CD -> AC + BD. Each chemical group (A, B, C and D) essentially switches partners.
Acid-base reaction: Observe that acid-base processes are a special case of double replacement. They can be identified by crystalline salt and "H2O" presence among the products. For example, sodium hydroxide (NaOH, a base) and hydrochloric acid (HCl) give sodium chloride---common salt---and water through the reaction NaOH + HCl -> NaCl + HOH (H2O). Here the chemical group formula is: A = Na, B = OH, C = Cl, D = H.
Combustion reaction: Identify combustion through unique reactant/product features. First, it has molecular oxygen (O2) as a reactant, but never as product. The other reactant is a hydrocarbon such as "C6H6" or "C8H10". Water (H2O) and carbon dioxide (CO2) are products of a combustion reaction.