Click on a building which you are in the process of upgrading.  You will see the increase in influence shown as the last figure towards the bottom of the window which opens.  The amount of influence each building (or knowledge) adds is a fixed amount unrelated to the length of time the upgrade takes.  So the increase in influence is the same whether you let the building or knowledge complete by effluxion of time, rush with spped-ups or complete immediately by purchase with gold.

If you wish to increase your influence as rapidly as possible you should focus on knowledge.  And within all the various branches of knowledge some, as for example Shaman knowledge, have noticeably high influence figures.

To a lesser exient training and retaining lots of troops also inflates influence.

A higher influence, by itself, confers little or no benefit so you might review whether aiming to increase influence as rapidly as possible is a good idea.

Thank for your aswer John.

I was not thinking about  increase my influence as rapidly  as possible, it was more of trying to work out what I need to upgrade to catch them up in the clan battles LOL

Ah, I see.  Well what I do is to browse the various knowledge trees looking for the available advances with the biggest influence figures.  As indicated above, Shaman is often good, I-V troops another and Hero.

If you have not yet maxed out Invaders that branch is deserving of priority and there are many high influence advances available late in the tree.

Buildings do not offer so wide a choice, for what it is worth, the Palace and the Wall offer a bit more influence than others.

Good luck with your CvCs.

Thnak you John.

That has given me a lot of info :-)😀