Friend visiting from the US

If she holds a US Passport, she will be able to stay up to 90 days. I do not think that financial means are an issue, since you are essentially guaranteeing her support (I do not recall ever being asked about my financial situation on entry to the EU, or my employment status) and her reason for traveling appears to be to visit you, a perfectly valid reason.

If she holds a passport from another Country, or has visited a Schengen agreement country recently, then things may change, more information would be needed.

if she is only staying 30 days no need for a visa
https://travel.state.gov/content/travel/en/international-travel/International-Travel-Country-Information-Pages/CzechRepublic.html

Having taken over 20 trips to Europe since 2002 the only country that ever asked about my finances, employment status proof of a return plane ticket and where I was staying was the U.K.

Watch out for the passport validity part i.e. at least 6 months. That can stop you at the border and if you are less than a year they may take it as an opportunity to ask a few questions so hopefully the "mental health" doesn't upset things.

This question cannot be answered definitively without knowing which country's passport the friend holds.

I'm sorry about leaving out that information. My friend holds a US regular passport, and this will be her first time travelling.

With a US passport visits to Schengen countries are visa free and allowed for up to 90 days (in any 180 day period). Financial status should not be an issue. The immigration/passport control officers normally ask 'what is the purpose of your visit?' to which you answer 'tourist' or 'visiting friend or family'. I have never been asked how long I'm going to stay, where I'm going to stay, or what my financial situation is. Now, they normally glance through the pages of your passport and, if you have some questionable country stamps in it, they might ask further questions.

All answers you got are correct. Up to 90 days US passport is sufficient. To enter Czech Republic is much easier than to enter USA. My educated guess is nobody will ask anything. In that very unlikely case they ask it would be where you are staying. She should know your address and phone.