Because I have experience, I did not have to make the comparisons that I will suggest. For IR spectra, I had used a book that listed the structural features with each band, but it also had example spectra. That is how I like to think.
For your IR spectrum, look to see if you have any of the characteristic stretching frequencies for different functional groups. I can see one functional group that is fairly easy to identify. Hint, your compound contains two oxygen atoms.
For your NMR spectrum, what group or groups can you identify from a chemical shift table? The integral shows two peaks. As I indicated earlier, the sum must be an even number. If the peak with the greatest chemical shift is one hydrogen, the other group of peaks must be an odd number, 1, 3, 5, 7, etc. By measuring the height, you should determine that one of those is in better agreement than the others.
If you were trying to identify your compound by joining the pieces you have identified, it will be like building something out of Tinker Toys. From the information you have before you, there will only be one possible structure.
If you lab book doesn't have your compound to compare with your spectra, you can go to
SDBS to find it.