What is a good way of analysing and interpreting a passage presented at an HL English Oral Exam?

What I like to do first is to read the passage and then go line for line and interpret what the author is trying to convey. First comment on the language and then on the deeper content. This can be especially difficult when analysing a Shakespearean passage since there are so many metaphors present and connotations to other scenes within his plays. 

Example:

Enter QUEEN GERTRUDE

How now, sweet queen!

QUEEN GERTRUDE 
One woe doth tread upon another's heel,
So fast they follow; your sister's drown'd, Laertes.

Similarities between Hamlet and Laertes – come home to same mess.

LAERTES 
Drown'd! O, where?

QUEEN GERTRUDE 
There is a willow grows aslant a brook,

Willow slanted towards brook and he was climbing on it to get flowers. 
That shows his hoar leaves in the glassy stream;

Soft leaves – NATURE – she belongs there. A creature apart from culture – ROTTEN DENMARK.

Hamlet ripped her from it. 
There with fantastic garlands did she come
Of crow-flowers, nettles, daisies, and long purples

Orchids – round roots – look like testicles that’s why shepherds give them foul names. 
That liberal shepherds give a grosser name,
But our cold maids do dead men's fingers call them:

People trying to categorize flowers – makes them ugly

DEAD MAN’S FINGERS: supernatural element – nature drags her down – young girls call them dead man’s fingers – live juxtaposed to death. She does not belong to this world so nature claims her back – this is like her nunnery. 
There, on the pendent boughs her coronet weeds

She is going to hung her weeds on the tree but she slipped and broke a branch. 
Clambering to hang, an envious sliver broke;
When down her weedy trophies and herself

The garlands and herself fall down like funeral wreaths – plunging to her death. 
Fell in the weeping brook. Her clothes spread wide;
And, mermaid-like, awhile they bore her up:

Supernatural element – mermaid – beyond human nature. Just nature, no struggles, no questions. Returns to nature where she belongs. – counter image of rotten kingdom of Denmark. 
Which time she chanted snatches of old lauds;

At ease with everything – old lauds = hymns from church – her own funeral. 
As one incapable of her own distress,

Does not feel own distress
Or like a creature native and indued

She feels at home there – familiar with that element – she goes with the flow because that’s what she’s been doing throughout the whole play, just there and be played with. 
Unto that element: but long it could not be
Till that her garments, heavy with their drink,

Her clothes drag her down – her sorrow and also the things that are not part of nature. 
Pull'd the poor wretch from her melodious lay
To muddy death.
sinks down into Denmark. We go back to corrupted world. Innocence is dragged down by the sorrow she feels in the place that is the muddy corrupted world of Denmark. 
LAERTES 
Alas, then, she is drown'd?

QUEEN GERTRUDE 
Drown'd, drown'd.

LAERTES 
Too much of water hast thou, poor Ophelia,

Too much sorrow did u have Ophelia – oyu have already cried for me – everyone’s sorrow was dumped on you and this is what dragged you down. 
And therefore I forbid my tears: but yet
It is our trick; nature her custom holds,

Nature is in one way but mankind acts in another – we don’t cry we ACT. – REVENGE.

He does exactly like HAMLET. We do human nature style – kill. 
Let shame say what it will: when these are gone,

When tears are gone – the woman who is connected to nature in me will disappear and then is the time to act. I will not be a woman to think (just like Hamlet) – im going to act straight away. 
The woman will be out. Adieu, my lord:
I have a speech of fire, that fain would blaze,
But that this folly douts it.

He’s going to speak in FIRE – revenge. The sorrow is pressing down on my rage right now, need to get rid of it. – FORESHADOWING. 

Exit

KING CLAUDIUS 
Let's follow, Gertrude:

Let’s do the same as Laeretes. He will kill Hamlet – all problems with be solved. 
How much I had to do to calm his rage!

He’s acting – has been provoking him and made everything seem worse… 
Now fear I this will give it start again;
Therefore let's follow.

FORESHADOWING – he’s going to take care of Hamlet – schemer – always manipulates the situation – as no true PERSONAL ACTION – no true AGENCY. 

Exeunt

Approach: 

Please note how I have commented on every stanza, illustrating double meanings and interpreting metaphors and symbols. This is especially helpful when trying to find out when and where the scene takes place within the play.

Now try the Iceberg Method:

The most evident: the characters – Gertrude, Lartes and Claudius, what they are talking about – the action (Ofelia picks flowers and drowns, Lartes is sad, Claudius enters)

The less evident: Lartes is Ofelias brother, Gertude is Hamlet's mother, Claudius is Gertude's husband. Gertrude tells Lartes in the nicest way possible that his sister is dead. Lartes is so shocked that he cannot even cry. Claudius wants Lartes to kill Hamlet.

The least evident: Put all the deeper analysis made within the passage together and get to a bigger conclusion – in this case – Ofelia is a creature of nature and mermaid-like, but in a corrupted environment such as the rotten Denmark seen in Hamlet's eyes. Therefore nature has come back to claim her. At the same time Gertrude describes her death in such a way to her brother in order to avoid feelings of revenge. However, then Claudius enters and manipulates Lartes into blaming Hamlet for her death, coming back to fire and rotten curruption.