Hi & Welcome
1) I can only find an overnight train from Amsterdam to Prague, even though I have read that there are day trains as well. Am I not looking in the right place? How can I find/book a day train?
As of now (and as far as we remember for many years already) the only direct connection between Dutch and Czech capitals are the overnight CNL train (19:01-9:27 and 18:29-10:03 on the way back). However it doesn't mean that you can't travel between two cities during the day - with one train change it is totally possible and quite easy actually, although overall travel time in this case will still be about 12 hours (depending on connection)
2) Is it best to book round trip from the Dutch Rail Line (NS Hispeed, is it?), or a one-way from the Dutch, and a one-way from the Czech Rail Line (CD)?
Well, here it's a bit tricky and you should look at the particular date of the journey and whether you choose to travel with direct overnight train or during the day with change. Because sometimes it might be cheaper to purchase ticket via NS website, sometimes via CD (Czech Railways), while sometimes even via
German Railways (DB) website 3) The fare I found while attempting to book from the Dutch website was over 300 Euros for 2 people - that can't be right, can it?
Again, it's hard to say something without knowing the exact date, but de-facto tickets for the direct overnight CNL train start from only 29 euro per passenger, however when cheapest fare level tickets get sold out the next price level kicks in and so on, until the full standard fare is reached (300+ euro for two passengers seems to look like the price for the full fare tickets). So with date relatively close from today you might not get a chance to purchase cheapest discounted tickets. That is why we suggest you to decide whether you want to travel for 12 hours during the day with one change or instead go with direct overnight option, then decide on the date and let us know. With this information we can definitely let you know where (NS, CD or DB) to buy your there and back tickets and what will be the cheapest fares available