Finite field as $F_p$ vector space

Question

I read GTM 167 Field and Galois Theory written by Morandi.In charpter 2 ,finite fields part, author claims that a finite field $\rm F$whose $\rm{Char(F)=p}$,$\rm p$ is a prime here,can be considered as an extension field of $\rm{F_p}$.I do not totally understand this part. $F_p$ does have characteristic p. However,how could we denmostrate that $\rm{F_p}$ is contained in $\rm F$? And the rest part says that if $\rm [F:F_p]=n$,then $\rm F$ and $\rm F_p$ are isomorphic as $F_p$ vector space,which shows that $|\rm{F}|=p^n$.Why there is an isomorphism here and how could we make the conclusion that order of $\rm F$ is $\rm p^n$? Hint is welcomed!