[General Notes] [Present Progressive] [Imprefect Progressive] [Future Progressive Tenses] [Other Progressive Tenses]

Use progressive tenses in order to emphasize continuity of an action or an event. To form progressive use estar/andar/continuar/pasar (el tiempo)/seguir + present participle, although estar is the most common. Many textbooks don't even mention the other verbs!
See conjugation of andar, estar, seguir.
For formation of present participle see conjugation of regular, irregular and stem-changing verbs. 
Use the present progressive tense -- estar + present participle -- (only!) when referrring to an action in progress.
+ present participle
Estoy escribiendo una carta (ahora!).

Use the imperfect progressive when referring to actions in progress in the past. It gives a greater emphasis to the ongoing nature of the action than imperfect. To form it use the imperfect of estar and a present participle.
+ present participle
Mi novio me estaba besando cuando mi padre abrió la puerta. 
One can use the future progressive and the future perfect progressive to make sertain emphasizes although it rarely happens. For example
Yo veré. I will look. Sometime, for sometime. Simple Future
Yo estaré viendo.  I will be looking.  Continued process  Future Progressive
Yo habré visto.  I will have looked.  By the time you arrive.  Future Perfect
Yo habré estado viendo.  I will have been looking.  Continued process by the time you arrive. Future Perfect Progressive

One can also form other progressive tenses to express conitnuity of an action, but in reality they are hardly used. For when they should be used, see the rules for the "paternal" tense. Just for the sake of it, here is what some of them would look like:
Preterit Progressive (used rather infrequently) Yo estuve estudiando
Conditional Progressive Yo estaría estudiando
Present Subjunctive Progressive Yo quiero que él esté estudiando
Imperfect Subjunctuve Progressive Yo estuviera estudiando
Pluperfect Subjunctive Progressive Yo hubiera estado estudiando
Present Perfect Progressive Yo he estado estudiando
Conditional Perfect Prgressive Yo habría estado estudiando