I have functional 3G connection on my Pi but I have to turn it on manually after each reboot in Sakis3g.
Does anybody know how can that be done automatically?
The easiest way to start a background process, or something that just needs to run quickly and set something up (such as networking), at boot time, is still to add it to
/etc/rc.local. I say "still" because it is was originally an aspect of the older init system on Raspbian (SysV) which has now been replaced by systemd. However, it is still supported for backward compatibility and almost certainly will be for perpetuity.
Note that it is not always as easy as it may seem; there is a collection of questions here already about it -- you may want to refine that search if you run into problems.
Beware that if this is something that doesn't go quickly to the background (say 5-10 seconds), you need to fork it (
&) so that it does, or you will screw things up.
Finally, this is a fairly comprehensive means of debugging problems.