Installing bearings is much easier than removing them.
The main thing is that you keep Bearings and surfaces Clean. Make sure that you don't get the bearing into contact with contaminant, and clean the surfaces before installation.
The another important thing - it might seem obvious - its to double check the dimensions of the bearing and the hole (fits and clearances). Usually, the bearing manufacturer has a pretty detailed manual with shaft tolerances depending on many factors (e.g. shaft diameter, type and magnitude of load etc).
Finally, the most important thing is handle bearings with care. If they fall on the floor, or have even relatively minor impacts, then the ball (or other rolling elements) can develop dents which will a) reduce the life of the bearing, b) make the bearing underperform.
There are a few installation methods. Sometimes all its need is the hand pressure (some even go as far as saying that, if you can't fit a bearing with the pressure of your hand you are doing something wrong).
The next step is mallet with a Bearing Fitting Tool
figure 1: SKF Bearing Fitting Tool Kit Hammer, TMFT 36-H (source indiamart)
Then there is the hot mounting method (this is usually for medium sized bearings. Essentially what happens is that you heat the bearing in order to increase its size and then you slide in the shaft. That has the effect that the bearing is then essentially pressfitted on the shaft
figure: SKF bearing heaters (source Wychbearings)
The final option is probably hydraulic mounting (although this is for much larger bearings).