ACEX1k

How come you're targeting an Acex1K? You'll get a lot more for your money with a newer family(unless you didn't pay anything in the first place.)

This is a very broad question. You can use SOPC builder to put a Nios soft processor into an FPGA and then write C for that(including use of the nifty C2H accelerator). But Nios won't go into an Acex1K(I don't think). There are third party tools that take C code and write out HDL. That's probably closer to what you want.

But it sounds like you're just getting started and my strongest recommendation is to sit down and learn Verilog or VHDL(If you don't care, look at Verilog since its syntax is closer to C). You don't have to be an expert, but it's important to get a feel for it and become comfortable with a hardware language. Why? Because C has been explicitly written for a serial processor, where a hardware language in an FPGA runs things in parallel. There is a world of difference between these two and unless you get your hands a little dirty writing in a parallel language, you're potentially in for a lot of difficulty(a lot more than if you had just rolled up your sleeves and learned an HDL in the first place). Once you have an understanding, then you can look into ways to write C for parallel hardware, and you'll be much more successful.

(I'm sure there are a lot of opinions on this topic...)