First time offender? :-) Not to make light of it, G‑d forbid! It's happened to me a couple of times, and I felt absolutely horrible. So I know where you are coming from. Nowadays, I try my best to prayer in a synagogue with a minyan, and that really helps to make sure that I don't forget.
The general rule of thumb: When a prayer is missed, in the following prayer one recites the Amidah twice.1 So if you forgot the evening prayers, then the following morning you would recite two Amidahs; the first one is for Shacharit (the morning prayers), and the second is "compensation" for the prayer you missed.
[In between the two Amidahs, wait a bit.2 In the case where you missed the evening prayers, ideally you should first recite the Ashrei which follows the Shacharit Amidah, and then recite the second Amidah.3]
The "makeup" Amidah must be said in the very next prayer. Otherwise, it's too late to compensate.
The compensation Amidah is always the same as the one it directly follows, even if this is different than the prayer it is replacing. For example, if one missed the Shabbat afternoon service, that night he would recite the weekday evening prayers twice.
A Musaf prayer which is missed can not be made up. Similarly, if one misses the morning prayer, then the afternoon Minchah is repeated, not the Musaf Amidah.
There are some other important details here that are worthwhile to review, so if you haven't already done so, we could arrange a learning partner with Jnet to study these laws with you.
Aside for the "technical" details mentioned above, as is the case whenever one neglects to do a required mitzvah, teshuvah (repentance) is necessary in order to spiritually make up for the missed mitzvah. Repentance means truly regretting your lapse in observance and resolving to be more meticulous about this mitzvah's observance.
Click here for more about repentance.
Rabbi Eliezer Danzinger for Chabad.org
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