It is quite easy if you read and follow the directions. The I-485 itself asks for basic information about the applicant. Staple two photos to the I-485. You should then fill out a G325 and and an I-643. Then attach proof of your asylum status (I-94, approval notice or immigration judge/BIA order), evidence of lawful entry (if you have it) and your birth/marriage certificates. Then some evidence that you have been in the US for at least one year since the asylum grant (do not overdo this) and if you have one, a copy of the RTD. If you are excludable, also fill out an I-602 for a discretionary waiver (if you need that you probably should retain counsel). Then put on top of the packet a check for the processing fee (the regular I485 fee plus the fingerprint fee).
You should not do your medical until told to do so.
You may also file any I-131 or I-765 at the same time.
You can put the forms for a whole family in one big envelop.
Send the application(s) to the Nebraska Service Center via certified mail, return receipt requested.