A systematic review is a type of research project in its own right. You are 'harvesting' information from a fixed set of research studies and collating it to make a sort of super-result. The important thing is to decide what the criteria are going to be for including a research study, then making sure that all of the research studies that meet those criteria are included. You look for the same kind of information from each study, then bring all the information together in your analysis when you write your review.
You need to start by deciding on criteria for selection (for instance, you might say all studies published after 1997, or all studies with a minimum number of participants, or you might set different criteria). This is different to a more narrative literature review, where you can choose to include or exclude studies because the research is interesting or especially relevant to what you are doing. You will have to explain in an introductory paragraph to the review what the criteria for inclusion were and why you chose them.
Once you have chosen the criteria and identified the research studies that fit those criteria, you need to make a list of the information you are going to look for in each study. For instance: how many participants, what methods were used, what were the findings? When you read the studies you need to look for that information. You are looking for results here, not analysis of those results.
A systematic review differs from an ordinary literature review in its purpose.
The purpose of a literature review is to review the sources that are specifically relevant to your research, considering how they inform your research methods and questions.
The purpose of a systematic review is to review all sources within a specified range against a fixed set of criteria.
These different purposes dictate different approaches in researching and writing. For instance, with a systematic review you will probably spend much more time considering the range to be examined and what the criteria should be. Writing up is likely to include more graphical representations of data (tables, graphs etc). Because of these differences, it is important to make sure you know which type of review you are being asked to undertake.
The Library has a step-by-step guide to Doing a systematic review, linked below.