I think the question will need to be more clearly stated to get interesting answers. Let's build up from vague to better questions. I hope that this exercise illustrates why asking a clearly-specified question is important.
How can I randomly select a passage from among 150 passages of text?
You can cut out the dice step entirely if you just write the text on the slips of paper instead, and draw random passages that way.
How can I generate uniform numbers from 1 to 150?
Use a computer.
How can I generate uniform numbers from 1 to 150 without a computer?
- Use your phone and navigate to
anydice.com or some dice rolling application.
- Write the numbers 1 to 150 on identical slips of paper, mix them up in a box, and draw them from the box.
How can I generate uniform numbers from 1 to 150 using dice?
Make a fair d150 and use that.
How can I generate uniform numbers from 1 to 150 using platonic solid dice?
Some answerers will make suggestions similar to those on RPG.SE about using different combinations of polyhedral dice.
Because there are so many ways to do this, it is probably too broad -- everyone will be tempted to post clever, or even cheeky, solutions without regard to practicality. (This is a very common occurrence for "brainteaser"-type questions. See Approximate $e$ using Monte Carlo Simulation and Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p? for examples.)
Insisting on using physical dice brings some additional complications:
- Can a good solution require a bit of arithmetic?
- Are the dice fair? Is compensating for possibly unfair dice part of the task? Some statistical questions assume fair dice, but since you're actually rolling physical dice, we ignore unfair dice at your peril.
- Can the user consult a table or other apparatus?
- Is minimizing the number of dice rolled important?
- Is the efficiency of the procedure in some other sense (such as the number of "rejected" rolls) important?
What's the most efficient way to generate numbers from 1 to 150 uniformly using a fair d6?
This seems like the best question to ask. Pretty much every house has a pair of d6 in some dusty cupboard, and this question generalizes reasonably well to arbitrary ranges of numbers.
Converting base-6 to decimal could be a stumbling block for some people, and if it is for you, then you'll have to state that and ask for an answer that doesn't using base-6 conversions (possibly returning to the domain of rolling several polyhedra.)
On the other hand, you could just renumber all of the texts using base-6 once, instead of doing the math for each dice roll. This will require less work if you’re doing more than 150 rolls.