I just bought a new samsung 840 evo 250gb ssd, it didnt come with the usb to sata conection adapter in which thje manual says ui have to connect for the migration of the data. now i have connected the ssd, but through my sata power cable and sata cable on my computer.. will it migrate with just this?
Yes it should work fine. The reference to USB is only if you want to migrate data using an external USB connection (eg using a laptop where it's not possible to connect a second hard drive internally on most models).
(Note: you don't get a SATA-to-USB adaptor with any drives, that's down to you. The drive manufacturer isn't going to waste money including something that most customers don't need).