Go learn how to use
ITA matrix.
Then use the booking engine or "bricks & mortar" travel agent of your choice to book your findings - ITA is a search tool, not a booking engine.... but it gives you more than enough information to spoon feed a booking engine or travel agent.... infact the last few times I've just ended up spoon feeding the airline's own in-house booking team details of all the sectors I need to book.
There is a learning curve, so prepare yourself to do
a lot of reading, and
a lot of testing but as free tools go, you won't find anything better. Kayak doesn't even come close to comparing !
There is another site called Hipmunk ... not quite as advanced as ITA, and it has become less interesting ever since one of their data providers (EVERBREAD) went out of business, so now you'll generally get similar results to Kayak because I think they use the same feed (Vayant .... if memory serves).
In terms of paid tools, ExpertFlyer is quite a good one because it'll list all the airfares for a route so you can see if there's a better deal to be had, so it can prove to be useful if you really want to dig down in to the nitty gritty detail of air fares ..... for example I've found a few instances where its cheaper to buy two one way tickets instead of a return ticket.... but its search function is simplistic and is no comparison to ITA. But at 99USD per year, if you do a lot of flying, its a handy cheap tool to have in the toolbox and useful in when used in conjunction with ITA. But most of the time, ITA comes up with either the best or "good enough" answers.... so as I said, its only really if you want that extra "edge".