The main thing before using derivative houses is to get a pretty comprehensive grasp of what phenomena each house covers. My handy reference book on houses and most things is Rex E. Bills, 1978, The Rulership Book, (American Federation of Astrologers).
In a very simplistic way (with complications to be mentioned subsequently), derivative houses work like this:
1. Let's suppose you want to know about your sister's money. In a simple way, your sister is represented by your third house, and money is represented by the second house.
2. Your sister's money would then be the second house from your third house, or your 4th house, because you always start counting from your house in question as number one. Similarly, if you wanted to know about your husband's (your 7th house) sister (a third house matter) , you would look to your 9th house, because you start counting as your house #7 as though it were house #1...your 8th becomes #2, and you wind up as the 9th as the third from your 7th.
3. OK, then if you want to know about your sister-in-law's money, you would look at your 10th house, as it is the 2nd (or money-house) from your 9th (your husband's sister.) I find it easy to miscount, which is why I use the Bills book, because he simply lists a lot of common derived house meanings.
4. You would then read these houses in your chart in the usual way. Are these planets tenanted? If so any afflictions or are the aspects harmonious? I work with house-cusp sign rulers, and might continue on with those.
5. The complicated part is that traditional astrologers coming from a horary tradition have assigned different houses to children depending upon their birth order, different houses to aunts and uncles depending upon whose side of the family they come from, and you have to decide which house cusp you intend to use for father and mother, whether the money of interest mightn't be an 8th house rather than a 2nd house matter, and so on.
There is a kind of logic to some of this, as a second child can be considered as the first child's (5th house) sibling (3rd house) which would explain why a second child in a family should be an 7th house matter.
6. I played around with derived houses and found the results to be mixed. But well worth learning, because sometimes someone is just dying to know something (her husband's girlfriend....) and you don't have the other person's chart to go on.
Happy astrologizing! W.