What follows is a collection of snippets that have been floating around in my head. I put them here so I can free up space for other, more important things
You will die and they will find you
One thing that you learn very quickly the hard way in wormhole space is that there is almost always someone watching you, waiting for you to make a mistake. There are many counters people develop to decrease their risk in space: closing wormholes, posting scouts, persistent dscan, combat probes, etc. All are good steps to take but some are ignored by wormhole residents to their detriment.
One common mistake for PvE pilots is believing that you are safe when you only see core scanner probes.
Rule #1: You see probes, you stop what you are doing and get to a safer location
Nearly everything in a wormhole takes place either at an anomaly (does not require probes to warp to) or a signature (does require probes to warp to). I have seen time and time again where people in a gas site (signature) believe that they can only be found or are at risk only from combat probes. Yes, sites do despawn from the probe scanner but usually only when you are basically finished. Until then, it only takes a close hit from a set of core probes to get a warp to. For a cloaky scout, that's all they need and usually they can do it in less than 10 seconds using dscan to estimate your location and increase the chance of a 100% hit on the probes before removing them from the system. In the time it takes you to notice, ask your fleet or corp about the probes, or otherwise consider your options, you are just as likely to already be seconds away from being dropped on.
Rule #2: Move off the warp-in
While basically required for gas and data/relic sites, many PvE pilots do not move from the warp in when they engage sleepers in w-space in combat sites. Doing this makes it all the easier for your potential attacker to engage you when they land in the site.
Rule #3: Dscan, dscan, and more dscan
Even with the new combat recon dscan immunity, you should be hitting this button more than any other in your EVE client. It is a tremendous intelligence tool helping you identify active towers in a system, look for abandoned towers with loot to steal, spot targets to hunt, alert you to incoming danger, find tractor units and depots, and a whole host of other benefits. It must be your first and most frequent action while in space.
You are the content
People new to wormhole space can often be overwhelmed with what to do even in a game where it is already common to be overwhelmed by choices. I think even more so than any other part of EVE, wormhole space is without a doubt what you make of it. While high-sec has content that can be consumed, low-sec has the backdrop of faction warfare to drive it and null-sec has the looming specter of sovereignty, w-space has none of those. It is truly an open book that you must write for yourself.
Do what you find fun. Above all else, enjoy your time in EVE. Whether you get the most enjoyment out of grinding down sleepers, building ships from raw materials, or exploring to the far reaches of your wormhole chain, do what you find most fun.
Be patient. Don't rush to judgement or unwise action. Bait is most often bait and danger can lurk behind every dark corner. If you take your time and are patient, you may, however, find some of the most exciting times in EVE at your doorstep. People less patient that yourself will instead be the one to make the mistake that benefits you.