There are two mechanisms (E1 and E2) for elimination reactions.
E2 mechanism:
The E2 mechanism has a bimolecular rate law (like SN2).
E1 mechanism:
The E1 mechanism has a unimolecular rate law.
Guidelines to relative rates of elimination:
In general
E1 and E2 pathways are both faster for tertiary halides than secondary halides, which in turn are faster than primary halides
E2 mechanism:
The E2 mechanism has a bimolecular rate law (like SN2).
E2 elimination reactions occur in a single step where proton removal by the base and expulsion of the leaving group occur simultaneously.
In order for the electron movement to occur in single step, the proton to be removed must be trans and anti (antiperiplanar) to the leaving group.
This means that if a pure diastereoisomer (such as meso-1,2-dibromo-1,2-diphenylethane shown below) is the substrate, a single geometric isomer of the alkene is formed.
In order for the electron movement to occur in single step, the proton to be removed must be trans and anti (antiperiplanar) to the leaving group.
This means that if a pure diastereoisomer (such as meso-1,2-dibromo-1,2-diphenylethane shown below) is the substrate, a single geometric isomer of the alkene is formed.
E1 mechanism:
The E1 mechanism has a unimolecular rate law.
The first step is slow heterolytic bond cleavage, as for the SN1 pathway. 
Fast proton transfer from the carbocation intermediate to the basic nucleophile in Step 2 then gives an alkene.
Fast proton transfer from the carbocation intermediate to the basic nucleophile in Step 2 then gives an alkene.
Guidelines to relative rates of elimination:
In general
E1 and E2 pathways are both faster for tertiary halides than secondary halides, which in turn are faster than primary halides
For the E1 pathway, this is because tertiary carbocations are more stable than secondary than primary carbocations.
For the E2 pathway, the more substituted halides give rise to more substituted alkenes which have higher stability.
For this E2 pathway, the rate may also be affected by the bulk of the base.
For the E2 pathway, the more substituted halides give rise to more substituted alkenes which have higher stability.
For this E2 pathway, the rate may also be affected by the bulk of the base.