Short answer: experiment, learn, read, learn, do, learn, read, experiment, learn, practise exams, do exam, get certification, done
Oh, and get some books along the way, about the subject. (e.g. networking essentials, or whatnot.. )
you need to have a fair bit of knowlegde on both areas, before you can even start doing exams. (there are thousands of questions in the exam pool, from which you get a series of questions presented during exams).
You can not be Linux certified, but you can get GNU/Linux certified. You can also be certified for a certain Distribution (e.g. Redhat or SuSE)
the choice is yours to make, what kind of GNU/Linux certification you are going for, and by which institute (e.g. LPI)
Same for the network admin certification, what type of certification do you want? (e.g. speciality in this area?)
Maybe you want to be specialized in Juniper™ or Cisco™, or generic?