So hacking in Eclipse Phase is somewhere between the lightspeed combat-decking of Shadowrun and the real-world tedium of cybersecurity and intrusion. Where the rules provide timeframes for infosec tests, they're given in multiple minutes -- 10 min to probe/defeat the firewall, for example. That can give you a sense of what a dramatic analogue the designers might have been going for: the heist.
From the character's POV, they're using tools and techniques they've picked up to intrude into a secure "facility" and alter or steal something from within. You can make up descriptions with varying degrees of technobabble, if it seems to suit the situation (low-babble example: "You realize that the idiot hasn't updated his protocols in eight months"), but the idea is to convey that the player is stealthily bypassing the oversight of an AI or other monitor, and/or passive counter-measures (read: locks and traps) that would impede progress. When I want (or have) to make an important system the focus of a narrative scene, I like to have notes about what would distinguish it to a security-savvy user (authorized or otherwise). Is it well-maintained or disorganized and obsolete? Are there lots of users, only a few (or one), or is it automated? What kinds of marks does that leave on the system? Was it created for this use, or is it repurposed? What does your Muse think of it?
However, there are some other important considerations. There's a reason why many other cyberpunk and transhumanist fictions go with a "combat" metaphor for hacking -- the tension of disabling a lock comes from the surrounding circumstances, not from the presence of a lock. If the character is hacking a passive system, especially something mundane like a device, it might be for the best to keep your descriptions brief and prosaic. In that line, I find Ghost in the Shell greatly informs my descriptions of action in Eclipse (heck, the Augmented Reality Illusion of EP is exactly a major plot point for GitS) -- it's better to keep the hacking off-camera as much as possible, and focus on describing the environmental changes that result from it, or, failing that, talking about how the goal is being advanced by the actions taken. Without the TRON-like narrative props of other systems and without taking time to generate notes about the specific peculiarities of the system being hacked, hacking really is about as interesting as making soup.
