I have seen in many web sites that the verb 'sortir' can be conjugated in the past with either 'être' or 'avoir'. What is the difference?
There are a few verbs that are composed with the verb être in the compound tenses (passé composé, plus-que-parfait, futur antérieur...).
You can memorise the most basic ones with the following mnemonic rule
MRS DR VANDERTRAMPP
Monter, Rester, Sortir, Devenir, Retourner, Venir, Aller, Naître, Descendre, Entrer, Rentrer, Tomber, Revenir, Arriver, Mourir, Passer, Partir.
Monter --> monté (went up)
Retourner --> retourné (returned)
Sortir --> sorti (went out)
Venir --> venu (came)
Arriver --> arrivé (arrived)
Naître --> né (was born)
Descendre --> descendu (went down)
Entrer --> entré (entered) Rester --> resté (stayed)
Tomber --> tombé (fell)
Rentrer --> rentré (went back in)
Aller --> allé (went)
Mourir --> mort (died)
Partir --> parti (left)
Passer --> passé (pass)
Another mnemonic rule is given here (the so-called La Maison d'être):
These are all intransitive verbs (that is, they have no direct object) that communicate a certain kind of movement.
(Note that the inverse is not necessarily true. E.g. Courir meaning run is conjugated with avoir. Also, e.g., voler (fly), rouler (roll), nager (swim), marcher (walk), sauter (jump). Therefore il a couru, nous avons nagé and so on.)
Normally all these verbs (MRSDRVANDERTRAMPP and their compounds-parvenir, repartir, remonter, redescendre, ressortir, etc.) are conjugated with être. However, the following verbs are a bit tricky.
Monter, Sortir, Retourner, Descendre, Passer, Rentrer
These can be used transitively (with a direct object), and when this happens, these verbs need avoir as the helping verb. In addition, there is a slight change in meaning.
Elle est sortie. - She went out.
Elle a sorti la voiture - She took the car out.
For more you may consult the following page
Être is also used to form the compound tenses of Reflexive Verbs and the Passive Voice of Transitive Verbs. E.g.
Je me suis promené(e). Le pont a été démoli. La porte était ouverte par le concierge.
Monter and descendre also take avoir in such expressions as:
Ils ont monté l'escalier. J'ai descendu la rue.
Note also that for a few verbs like demeurer, changer, grandir, vieillir (respectively, change, stay/remain, grow, pass, grow old), there is a difference in meaning between expressing action (conjugation with avoir) and state (être). Cf.,
Il y a demeuré pour soigner sa mère (action).
Il est demeuré insensible à nos prières (state).
Elle a beaucoup grandi au collège (action).
Comme elle est grandie (= Quelle grande elle est) (state).
La journée avait passé tranquillement (action: had passed).
Le danger était passé (state: had passed-was past).
Above may be used as guidelines for further reading.
See also the relevant discussion here
(thanks @jlliagre for pointing me out this discussion)