Once you complete your masters, you are qualified to apply for a PhD (although some courses and universities allow you to apply for a PhD directly, with the understanding that you will begin with a masters and transition into the PhD).
In order to apply for a PhD, you need to do the following:
1. Decide on a research topic and prepare a research proposal in accordance with the standards in your field of study. We advise you to share the proposal with your current masters supervisor or anyone (preferably an academic) who knows about your field.
2. You need to aggressively search for a supervisor who is an expert in your research area. Note that you might have to be strategic about your choice of supervisors. It is possible that you might adjust your research interest slightly in order to appeal to certain supervisors.
3. Find out the procedure for applying to the PhD. Some schools encourage you to contact potential supervisors and some expressly say that you should not. If you are advised to contact potential supervisors, ensure you draft an excellent email that details your research interests and research question, the experience you have in your field and most importantly why you want to work with the supervisor. Note that if possible, you should also hint that you have something to offer the supervisor. For example, you can offer perspectives on a topic from a developing country, or you are able to undertake a comparative analysis based on your experiences in a particular field. People are more likely to respond if they feel you will be an asset to them.
4. Submit an excellent application and ensure you apply to more than one school to increase your chances.
Good luck!