$\text{HBr}$ reacts with ${\text{CH}}_2=\text{CH}-{\text{OCH}}_3$ under anhydrous conditions at room temperature to give:

This is an electrophilic addition reaction. The proton (${\text{H}}^{+}$) from $\text{HBr}$ adds to the alkene.The reaction follows Markovnikov's rule, but more importantly, it forms a carbocation stabilized by resonance with the adjacent oxygen atom.
$${\text{CH}}_2=\text{CH}-{\text{OCH}}_3\stackrel{{\text{H}}^{+}}{\to }{\text{CH}}_3-{\text{CH}}^{+}-{\text{OCH}}_3\leftrightarrow {\text{CH}}_3-\text{CH}={\text{O}}^{+}{\text{CH}}_3$$
The nucleophile ${\text{Br}}^{-}$ then attacks the most stable carbocation:
$${\text{CH}}_3-{\text{CH}}^{+}-{\text{OCH}}_3+{\text{Br}}^{-}\to {\text{CH}}_3-\text{CHBr}-{\text{OCH}}_3$$