Every country has own selection procedure. I know about some countries.
In UK and Australia, You can do direct email your CV to respected prof. If he /she will be interested in your profile. You will have to write research proposal for getting schorship. for UK, you need a good TOEFL or IELTS score.
I would like to tell that there are some college scholarship or some common scholarship. But, getting a scholarship is not an easy task. Some PhD are self funded too.
In France , Germany, spain and Italy, you will have to apply the phd opening position. You must be search for each and every university as per your research interest. Every lab has own criteria. Some prof ask for only CV and cover letter or some ask for CV, SOP, LOR and transcript. If they will like your application then they can direct give you mail for skype interview.
For Germany, you can qualify DAAD schorship. After getting this scholarship you will 100% get good university for PhD.
In Sweden , you will have to fill application for particular PhD opening. They need transcripts, contact detail of two References,CV and Motivation letter.
All the best !!
PS: GRE is an exam not any impossible task it's better to give GRE. Exam like TOEFL and GRE will enhance your confidence.
Always remember, Limitations only exist in mind.
Mohini Mishra, Science Foundation of Ireland awarded Researcher
Source: Quora Digest