look at the reagent first. It seems intuitive to decide between SN and E first, but it's not a good idea. Start by deciding between 1 step and 2 step and two step mechanisms.
If it's a strong base, start thinking bi-molecular. If you have something that really wants to attack, then there won't be time for carbocation formation. Also note the size of the base. Is it bulky like t-butoxide or small like Ethyl oxide? Bulky is elimination.
Next look at the substrate. If you have methyl or primary and a good leaving group, it's SN. If it's tertiary and If you can get an anti orientation from one of the Beta Hydrogens, go with E2, especially at high temp.
If you have a weak reagent, then it's going to sit there and chill until something is really attractive like a positive charge draws it to attack. If it's a tertiary substrate, look for heat to be the giveaway for elimination.
Also with reagents, some can be nucleophiles but not bases. Know which ones these are.