I'm going to try and attend my very first Vespers service at an Orthodox (OCA) church this evening, and I was wondering what to expect.
I've been reading midweek Vespers services at church for many years, and I simply don't know how to answer this question. There are A LOT of details I could cover, A LOT of different ways I can go with my answer. And yet, having never been to a midweek service, you probably don't even know how to refine your question. Let me therefore do what I can to keep my answer brief and focused on the big picture without going into too much detail.
I would counsel you to expect a service of about 30-45 minutes. You'll hear a number of Psalms read: Psalm 104 after the opening prayers, Psalms 141, 142, 130, & 117 as the priest censes the church and the choir intersperses some hymns for the saint of the day, a short passage from Psalm 54 midway through the service with maybe a lesson from the Old Testament immediately following, and Psalm 123 as the choir sings a few more hymns for the day. (All Psalm numbering given here according to the Masoretic Text usage found in most Protestant/Catholic Bibles) Interspersed throughout this Psalmody, you'll hear a number of litanies ("Lord have mercy!"), a hymn worshiping Christ the joyous light of the Father (one of the oldest hymns still in use in the Church, with documented use as early as the second century), and the song of St. Symeon (Luke 2:29-32). The service will then finish with three troparia: the troparion to the saint of the day, the troparion for the day of the week (to the Holy Apostles on Wednesday nights), and a troparion to the Theotokos; another litany; and the dismissal.
I hope even this simplistic structure of the midweek Vespers service isn't too much for you to process, since I tried to pare it down as much as I could. Without overloading you even more, all I can say is go to the service with a spirit of prayerful openness to what you'll experience there. I hope you have a wonderful time there and maybe even a chance to meet the priest. The midweek Vespers service is one of the shorter offices of the Church, shorter than the Saturday Vespers, so it's definitely one of the best places to start experiencing Orthodox liturgy. May your visit be fruitful.