How are we able to determine the time a fixed star takes affect? Aspects I believe can be determined by planetary returns.

I have caput algol twice in my chart, each on the same degree, and it is rather concerning. Especially when I don't know when to watch my back.

Also, if it is conjunct the 4th house and in opposition to the 10th, how can I interpret this? How would this star impact these houses?

Apply the nature of the star to the natures of those houses. Caput Algol is one of the most violent stars, you should watch out for situations that relate to the houses. These could manifest negatively. As far as timing, I'm not entirely sure.