There are many good papers on LDO by Rincon Mora. Just google - LDO Rincon Mora... you ll get enough papers.
First u need to design an opamp ( p - input ) and then use it in negative feedback mode. you ll find the circuit diagram in Rincon Mora papers. Its the standard circuit.
You can go for pmos drop-out element or nmos drop-out element depending on your outout voltage. if u use nmos drop-out element , there are no stability issues but maximum output voltage u can get is one vt less than supply. If u want higher output voltage, u have to go for pmos drop-out element but there r stability issues. u have to use compensation.
regards
cinch