I'm not widely traveled, but I've been to a bunch of different synagogues of all the major flavors, often as one-offs, including C and MO, so I'm answering on the basis of that experience.
You can just show up.
Many of the factors that affect you are the same between Conservative and Modern Orthodox synagogues. The Conservative synagogue you've been going to might or might not be egalitarian, which would make more of a difference if you were a woman.
In either, as a man you would count for the minyan if you were Jewish, so take a look around when you get there. If there are more than about a dozen men you probably don't need to worry (I'm fudging that number because, hey, you might not be the only non-Jew there). If the number is close, look around for the gabbai, the person who seems to be coordinating logistics like handing out aliyot, and tell him you don't count. Since you're new he may approach you first; if he offers you any honor, like an aliyah, decline. If he inquires, just tell him you aren't Jewish and that will take care of it. Optionally you can also tell him that you've been going to such-and-such Conservative shul (if it's near enough that people would know it), which tells him that you aren't a complete newbie (you don't need to have the service explained to you).
At the kiddush, if wine has been put out for everybody it will probably be in individual cups. If so you can freely take one. If there's a bottle and people are pouring their own, you should skip it or wait to be offered a filled cup. It's probably mevushal, meaning that being touched by a gentile won't be a problem, but you never know. There are wines that can be made ritually invalid if handled by gentiles. (Sorry about that.)
In my experience any newcomer at any type of synagogue gets asked "new in town?" or the like. You can say you're just visiting; you might be asked who you're visiting as people try to play "Jewish geography". You can say you're shul shopping (if you are). Most people won't want to know details of your personal status.
When mingling with people (like at the kiddush), don't offer handshakes to women. More generally, take your social cues from the other men there.
As a non-Jew you are not forbidden to drive on Shabbat, but it will be less awkward for you if you park a block or so away instead of right in front of the building.
If you decide to go to this synagogue on a regular basis, it's a good idea to talk with the rabbi. (Call during the week and make an appointment; don't try to do it at the kiddush.) Explain your intentions (I can't tell if you're considering conversion, for example) and ask him if he has any problem with you coming there. Not only is this polite -- if you're going to join a community it's good to introduce yourself -- but he may be able to connect you with others, e.g. for meals.