Installing Convex.jl is a one step process. Open up Julia and type :
using Pkg Pkg.update() Pkg.add("Convex")
This does not install any solvers. If you don't have a solver installed already, you will want to install a solver such as SCS by running :
To solve certain problems such as mixed integer programming problems you will need to install another solver as well, such as GLPK. If you wish to use other solvers, please read the section on Solvers.