Some hints I give to my students on how to structure a literary/text analysis, be it for a oral presentation or a written essay:
1. Focus on one specific issue (theme/gender/narrative style/characters/symbols etc) and state this issue when beginning to write or talk about it.
2. Gather evidence in the form of quotations (or in the picture book case possibly also illustrations) regarding that specific issue and use that to help argue your case or show that what you've decided to look at makes sense.
3. Draw parallels to an ideology or a theoretical framework, which will provide you with a link between the specific and the general and help you establish the relevance of your work/viewpoint.
4. Sum up your argument in a coherent conclusion, that shows the results you have come up with with clear ties to your initial question/issue/focus. Tie up your argument/idea.
This is a fairly basic formula for academic analysis and I don't think it's that complicated. In general I advise my students to be brave, take a stand of some kind and make sure that their choice of evidence reflects that. Then they will have to show why this is relevant on a more general level before they sum up their analysis. I usually end by asking them to pleeeeease say something interesting!