As mygamingid said, it all depends on the why.
If you want to play a wizard that is doing everything to get the new technology working for him, then that is at least going to be his high concept, and every bit of magic he uses should be dedicated to that, enchanted items, potion slots, rote spells, everything. He would be a research wizard more than anything else. If it would be easier, Harry would probably know about it, especially given Luccios interests on the subject.
A different approach (that I have been working on) would be: "Any sufficiently advanced technology magic is indistinguishable from magic technology.". I also think this would be the way for a wizard to go, because it seems much simpler to research this than the magic described above. I would still require him to devote most of his concept to the research of this magical construct.
The problem is not the internet itself. Those machines are far away and have nothing to fear from the murphionic field. The only problem would be accessing the internet.
First there is the need to build a magical computer. You should probably start with a basic operating system. It should be able to interpret your input and display it at the same time. And it should be adaptable, so you wouldn't have to start from scratch if you want to change something. I would take a mirror as a starting point. A mirror in a frame, the frame has lots of wholes that can later be filled with magiced (programmed) gemstones to add functions. You can use the mirror as a touchscreen, and you can use a magic marker (which would actually be magic) to write on the mirror, and it absorbs the text so you can send it or safe it or whatever you want to do.
With the basics set like this, you can add more functions. To access the internet, you need magic that understands the internet. So you need to create a magical program for your mirror, that takes over the job a browser would do. Once that is set up, you need an internet connection, a magical device that can connect to the internet, a magical modem if you will. I would set this up to be an optic fibre connection, because I assume the murphionic field won't interfere with light, and magic would probably have an easier time to create a distinct pattern of light than electronic patterns.
This should be the basics to get started with an internet ready mirror. Input and display methods could certainly vary, depending on your style, but that would be the basics, I think. The biggest problem would be, that you have to be a master thaumaturgy crafter as well as a master in computer science, because you would have to create every program yourself (including such things as flash, java, everything).
You could add other things as well. Levitating quills as a printer for example. Or a large map that can be made interactive with a google maps gem. Any kind of different programs.
Although I have to admit, it just wouldn't seem Dresdeny. On the other hand, there was the starwars-informationball-thing Morgan used in SK. I think if there was a reason to do this, there is a way.
But I have to say, that would be a concept that is cancelling itself out. You are creating problems with one aspect that you are trying to solve with the rest of the characters concept. So the whole strength of the character would be in cancelling out the inconveniences his other strength carries with it, and in the end he wouldn't be good at anything. Unless you can think of an adventure that would require this particular set of skills. I could see a character like that as an npc, though.