Learn Turkish: Yarışma yarın saat ikide başlıyor. - The competition starts tomorrow at two o'clock.

İkide means "at two" (the number iki plus the locative suffix -de meaning "at"). The ordinal suffix is -(i)nci. If the sentence were about the "second" competition rather than the time it starts, it would use the ordinal number: İkinci yarışma (The second competition).

How does the phrase saat ikide work to mean "at two o'clock"?

Saat means "hour" or "clock". When stating the time an event happens, you use saat followed by the number, and then attach the locative suffix (-de or -da, meaning "in", "on", or "at"). So, iki (two) becomes ikide (at two).

Why do we use the present continuous tense başlıyor (is starting) if the event is happening yarın (tomorrow)?

Just like in English ("The competition is starting tomorrow"), Turkish frequently uses the present continuous suffix (-yor) for fixed, scheduled future plans. You could also use the future tense (başlayacak), but başlıyor is very common and perfectly natural here.

The dictionary form of the verb is başlamak (to start). Why is it spelled başlıyor and not başlayor?