P-Trap installation

[Superandy64]

I just installed a new sink for my first time and everything looks good but I don’t know how to do the new P-trap. I bought an ordinary P-trap thinking that will work but it’s too small to attach to both ends and it’s seems to be too big to connect to the waste pipe. How should I go about this? I think the waste pipe is 1”? Also, should I cut down the waste pipe so it’s not going downward and just sticking straight out? Whiteish pipe is waste pipe and black pipe is sink.

 

[CT18]

Put the P trap together to see how close you are to the sink tail piece. You look to have half of an 1 1/2" bag trap in the picture. The trap will connect to that piece in your pic with a jam nut without the washer