In many cultures, a day is not always a 24-hour day. For example, in English we say that "this happened in the day of my grandfather." We also say, "It will take you a day to get to your destination" without meaning "exactly 24 hours." Also, "day" actually means 12 hours as the other 12 are a night.
In Jewish times, a day could also mean "a portion of a day." Let's see an example: In the days of Rehoboam, successor of Solomon to the throne of Israel, some representatives of the people headed by Jeroboam submitted a request. Rehoboam asked Jeroboam to go away for three days and then come back for the answer. (1 Kings 12:5) Did the people come back AFTER the three days? No. The account says they came back "the third day." (verse 12) Actually, this same verse 12 says that they came back because the king had said "come back the third day". But the king had said they should go for three days and come back AFTER. So we either have a contradiction or we understand that they understood the third day as being only a portion.
Again, the Jewish priests asked that Jesus' tomb be made secure until the third day because Jesus had said he would die and after three days he would rise from the dead. If they had understood it as we do now, the tomb should have been secured the fourth day.
So Jesus would be in the tomb for one full day and a portion of the first day and a portion of the third day.
Before we count the days, let's mention a few necessary facts.
(1) The Jewish Passover was celebrated on the 14th of Nisan. It could fall on any day of the week.
(2) The next day was always considered a Sabbath. (Leviticus 23:5-7)
(3) When the day after the Passover and the weekly Sabbath fell on the same day, that day was called "high" (King James) or "great" day. (John19:31)
(4) The day before the Sabbath was called "Preparation day". The other days only had numbers.
(5) Jesus died on the Passover day and the next day would be "a great Sabbath" according to John.
(6) The Jewish way in Jesus' time was to divide the daylight into 12 hours starting at around 6am. (John 11:9)
(7) The Jewish day started at dusk and ended at the next dusk.
Now, let's count the days of Jesus' death account.
1. Our Thursday:
At 6pm the Passover day and the Preparation day start. Around midnight the Passover lamb is eaten and then Jesus is arrested. He is interrogated all night and around our 11 o'clock in the morning he is nailed to the cross. Luke 23:44 mentions hour 6 and hour 9 (Jewish count). Hour 6, counting from our 6pm, corresponds to our 12 noon. Darkness falls. Hour 9, or our 3pm is Jesus death. The next Jewish day (Sabbath) would start at our 6pm. So we have a portion of 3 hours of the FIRST DAY. Sabbath starts at 6pm.
2. Our Friday:
Sabbath continues and Jesus is in his tomb. All is quiet; it is Sabbath. At our 6pm Sabbath ends and the first of the week starts. The SECOND DAY ended. It is dark, so nobody goes to the graves.
3. Our Sunday:
Early in the morning some women go to the tomb to attend to Jesus' body only to find that he had risen from the dead. (Luke 24:1) So we have a few hours of the THIRD DAY.
This way, Jesus was three days dead, which was actually a full day and two portions of days.
In the different accounts around Jesus' death, there are some apparent descrepancies or contradictions. There are explanations for all of them. But they should be dealt with as separate questions.