Software
Most scientific maps are made with software that is specifically intended for map design, such as ArcMap (ArcGIS) or QGIS. These programs are preferred as they allow for georeferenced plots of multiple layers of raster and vector files. However, the final design and editing of maps made in GIS software is often done in a vector editing program such as Adobe Illustrator, or InkScape (Tools for creating figures).
As a beginning MSc student, you may or may not have experience with using GIS software. Depending on the type of course or project you need to make a map for, it may be necessary to learn how to work with GIS. In many other cases, it may be sufficient to edit an existing map and include your own observations. In that case, make sure you have a high-quality image to begin with and keep in mind the information you need to include to make it legible and useful for your purpose. If necessary, you may ask your supervisor or a colleague to include the most important aspects for your map in GIS and to send you their map so you can edit it in a different type of software.