Well it depends on what all is available to you. Since you have not provided adequate information here are a few random suggestions.
1) If you have Wifi then simply connect both systems to the router and you will be able to access one computer from another and vice versa.
2) If you have an ethernet cable (not a cross) then you will be able to connect both the system directly.
3) If you have an external drive then copy from old and paste into new
4) There are certain laptops(old ones) which have a SATA port. If you laptop does have one then remove HDD from old PC and connect to laptop via SATA cable.
5)Cloud. upload the required files onto a cloud drive (Dropbox, One Drive, Google Drive etc) and the download on to laptop.
6) Use Team Viewer on both systems and transfer files.
See what suit you the best. Wifi or Network transfer is by far the easiest. then the external HDD transfer.