I often see prices on exchanges that look something like XRP/BTC or ETH/XRP... and I'm not quite sure how to interpret it. What does this mean, exactly? (I'm finding it difficult and confusing to buy coins when prices are listed this way).
ETH/XRP is the price of ETH in terms of XRP. It means that you can trade ETH for XRP (or XRP for ETH) and you get that number of ETH for every XRP. You will generally see the largest volume or most liquid coins on right side. Because making every possible combination of trading pairs available is not feasible (or even desirable), an exchange will only have a few currencies on the right, such as USD, BTC, LTC, ETH, and XRP.
Also, what does it mean when I see a "ETH/XRP" chart? Let's say the chart is in an upward trend -- does that mean XRP is rising compared to the price of ETH? (Or do I have it backwards?)
Again, ETH/XRP is the price of ETH in terms of XRP. If you see an upward trend you know that ETH is growing in value compared to XRP, though they could both be falling in value compared to USD. If you see a downward trend, you know that ETH is falling in value compared to XRP, though they could both be rising in value compared to USD.