I presume by injectable you mean the depo injection which you have every 3 months. Changing from this to the oral contraceptive pill is fairly straight forward. You start taking your pill from the day you should have your next injection. Doing it this way usually covers you straight away without any gaps.
I write the next bit being not sure if you are familiar with the oral contraceptive pill. There are 2 types of pill. One which is predominately oestrogen, this is the most commonly used by doctors and the other predominately progesterone, usually called the mini pill. The oestrogen version is taken every day for 28days and then you have a 7 day break before you start taking it again. During this break you should have what they call a withdrawal bleed, which resembles a period. The mini pill is also taken every day, but without any breaks at all so it is likely that periods will stop.
Before you decide to change consult your doctor or practice sister as they will have all the details you require and the best information as to which is best for you, not all pills suit everyone.