Since you do not specify which soliloquy you would like to analyze and there are several, let me help you analyze one soliloquy. You will then be able to apply it to the soliloquy you have in mind. Since the soliloquy Juliet speaks just before she drinks Friar Laurence's potion is her longest (IV.iii.15-60), it is a good one to analyze.
The first thing to look for when trying to determine both feelings and meaning is diction. What are the words she uses? For instance, Juliet opens this speech with the important word "farewell." This one word alone tells us that she is feeling the importance of what she is about to do. She understands fully that if her plan works, she may never see her mother or her Nurse again. Also, she realizes that if the plan were to fail, either because the potion truly killed her, or the potion failed and she had to kill herself, once more, she would never see her family again. In part, this is a goodbye speech.
Other important diction to look at is "faint,""cold,""fear" (16). These few words tell us that she is terrified. She is terrified of drinking the vile because it may be poison in disguise; she is terrified that it will not work and she'll be forced to either marry Paris or slay herself with the dagger; she is also terrified of waking up in the tomb. Also, the fact that the word "fear" is repeated four times, again, shows us just how terrified she is feeling (16, 29, 34, 52).
Another thing to look for when interpreting feeling and meaning is imagery, any image that paints a clear picture in a reader's head. One image is "stiffled in the vault," which shows us that she is terrified of suffocating in the tomb. Other images are "buried ancestors" and "bloody Tybalt" (43, 45). These images show us how terrified she is of laying amongst the dead, especially her newly killed cousin, whom Romeo "did spit his body / Upon a rapier's point" (58). The word "spit" in this line refers to a skewer and shows us that she is terrified of Tybalt's spirit seeking revenge while she is in the tomb.
All in all, the diction and imagery found in this soliloquy show us that Juliet is feeling terrified at this point and predicting future doom.