Unfortunately, the department does not have sufficient funding to provide substantial scholarships. However, the Faculty of Arts (of which the department is a part) has a scholarship programme for outstanding students and the university has need-based scholarship program. These scholarships will unfortunately only cover around a third of your living costs at most. You can also apply for a student grant, where the money is more substantial. However, since the grants are awarded based on presenting a scientific project, this is usually practical only in the later stages of your studies.
Every PhD student is eligible for governmental support (6000 CZK of non-taxed income per month). However this will cover only around a third of the monthly living expenses. PhD students can also apply for grants from the University Grant Agency which typically include a monthly non-taxable stipend of up to 10 000 CZK.
Currently, the department also offers a salaried PhD position.