Whether it's a romantic engagement or dinner with friends or colleagues, making an appointment (約束, yakusoku) is a vital part of everyday language in Japan as much as anywhere else. The grammar involved isn't too taxing, though the vocabulary extends as far as your interests. Meeting for coffee (コーヒー, kōhī) might be easy enough, but swot up on suitable expressions if your companion's hobbies include something more outlandish.
The main particles at play when organizing a schedule are ni (に) and de (で). Ni has several meanings, but we're concerned with two in particular.
First, ni can indicate the time of an event. For example, eiga wa jyūji ni hajimarimasu (映画は十時に始まります, the film starts at 10 o'clock). Time references relative to the present, such as kyō (今日, today), ashita (明日, tomorrow) and kinō (昨日, yesterday), are not preceded by ni. For example, kyō eiga wo mini ikimasu (今日映画を見に行きます, Today I'll go watch a film). Also exempt are expressions that define regular intervals, such as mainichi (毎日, every day) or the word for "when" (いつ, itsu). When referring to an approximate time, use goro ni (ごろに) or gurai ni (ぐらいに): Eiga wa jyūji gurai ni hajimarimasu (映画は十時くらいに始まります, The film starts at about 10 o'clock).