Can You Fast the Day before Ramadan?
Question

I heard that it is not permissible for us to fast before Ramadan. Is that true?
Praise be to Allah.Fasting in the second half of Sha`ban
There are hadiths narrated from the Prophet (peace and blessings of Allah be upon him) which forbid fasting in the second half of Sha`ban , except in two cases: 

Those who have a habitual pattern of fasting, such as a man who usually fasts on Mondays and Thursdays – he may continue to do so even in the second half of Sha`ban. 
If he joins fasts in the second half of  Sha`ban to the first half, i.e., if he started to fast in the first half and continues to fast until Ramadan begins, this is permissible. 

These hadiths include the following: 

Al-Bukhari (1914) and Muslim (1082) narrated that Abu Hurayrah (may Allah be pleased with him) said: The Messenger of Allah (peace and blessings of Allah be upon him) said: “Do not anticipate Ramadan by fasting one or two days before it begins, but if a man habitually fasts, then let him fast.” 
Abu Dawud (3237), al-Tirmidhi (738) and Ibn Majah (1651) narrated from Abu Hurayrah (may Allah be pleased with him) that the Messenger of Allah (peace and blessings of Allah be upon him) said: “When Sha`ban is half over, do not fast.” (Classed as sahih by al-Albani in Sahih al-Tirmidhi, 590 )

Al-Nawawi said: 
“The words of the Prophet (peace and blessings of Allah be upon him), “Do not anticipate Ramadan by fasting one or two days before it begins, but if a man habitually fasts, then let him fast,” clearly indicate that it is not allowed to anticipate Ramadan by fasting one or two days before it begins, for those who do not have a habitual pattern of fasting or who are not continuing to fast after starting to fast before (in the first half of Sha`ban). If one is not continuing to fast or does not have a regular pattern of fasting, then it is haram.” 
Fasting the day of doubt

Al-Tirmidhi (686) and al-Nasai (2188) narrated that ‘Ammar ibn Yasir (may Allah be pleased with him) said: “Whoever fasts on the day concerning which there is doubt has disobeyed Abu’l-Qasim (peace and blessings of Allah be upon him).” 

Al-Hafiz said in Fath al-Bari: 
“It was understood from this that it is haram to fast the day of doubt, because the Companions would not say such a thing based on personal opinion.” 
The day of doubt is the thirtieth of Sha`ban if the new moon cannot be seen because of clouds etc. It is called the day of doubt because it could be the thirtieth of Sha`ban, or it could be the first day of Ramadan. It is haram to fast on this day, unless it coincides with a day on which a person habitually fasts. 
Al-Nawawi said in al-Majmu’ (6/400) concerning the ruling on fasting the day of doubt: 
“If a person observes a voluntary fast on this day, and he has a reason for doing so, such as having the habit of fasting every day, or of fasting alternate days, or fasting on particular days such as Mondays, and it happens to coincide with that day, then it is permissible for him to fast on this day; there is no difference of opinion among our companions regarding that. The evidence for that is the hadith of Abu Hurayrah: “Do not anticipate Ramadan by fasting one or two days before it begins, but if a man habitually fasts, then let him fast.” If he does not have a reason, then it is haram for him to fast on this day.” 
Shaykh Ibn ‘Uthaymin said in his commentary on the hadith “Do not anticipate Ramadan by fasting one or two days before it begins…”: 
“The scholars (may Allah have mercy on them) differed concerning this prohibition and whether it meant that this is haram or makruh. The correct view is that it means it is haram, especially on the day of doubt.”  (Sharh Riyad al-Salihin, 3/394) 
Categories of fasting in the second half of Sha`ban 
Based on this, fasting in the second half of Sha`ban falls into two categories: 

Fasting from the sixteenth until the twenty-eighth. This is makruh, except for those who have a habitual pattern of fasting.
Fasting on the day of doubt, or one or two days before Ramadan begins. This is haram, except for one who has a habitual pattern of fasting.

And Allah knows best.