1. to settle, reconcile, make up 
[verb]
[bij-leg-gen, leg-de bij, bij-ge-legd]
"Bijleggen" is what people do when settling a dispute, or when making up afterwards. Note that when using this verb, you need to add the article 'het' which implicitly refers to whatever dispute you are settling; check out the examples.
"Bijleggen" is less used when it regards more serious occasions of dispute; in that case you may encounter words such as "verzoening" (reconciliation), "zich verzoenen" (to reconcile), "conflictoplossing" (conflict resolution).
Another translation of "bijleggen" is given in 2. below.
Examples:
– "Het akkefietje was onverwachts op een ruzie uitgelopen, maar beide partijen hebben het gelukkig snel weer bijgelegd."
("The quarrel had turned into a fight unexpectedly, but luckily both parties made up again quickly.")
– "Wordt het niet eens tijd dat jullie het bijleggen, dit conflict duurt al veel te lang!"
("Isn't it about time that you (guys) settle things, this conflict has been going on for much too long now!")
– "En?" – "We hebben het bijgelegd. Het berustte allemaal op een misverstand."
("And?" – "We've resolved everything. It was all due to a misunderstanding.")
Expressions:
– "De strijdbijl begraven": to bury the hatchet.
– "Zand erover!": let's forget it! Let bygones be bygones, etc. Literally: "cover it with sand!"
Example:
– "Ok, zand erover, we beginnen met een schone lei!"
("Alright, let's forget it, we'll start (again) with a clean slate!")
Related words:
– Conflict: conflict [noun] [het conflict, de conflicten].
– (Het) Goedmaken: to make amends, to reconcile, to make up [verb] [maakte goed, goedgemaakt].
Example:
– "Na een fikse ruzie hebben Franka en Casper het weer goedgemaakt."
("After a hefty fight, Franka and Casper made up again.")
– Oplossen: to resolve [verb] [loste op, opgelost].
– Verzoening: reconciliation [noun] [de verzoening, de verzoeningen].
Extra:
The picture shows Rudi Völler and Frank Rijkaard in the 1988 European championship football/soccer semi-final between West-Germany and the Netherlands. The Netherlands moved on to the final and beat Russia which is the only time we ever won a (football) final. It is said that both players "hebben het bijgelegd" after the match 🙂
2. to contribute, compensate/make up (financially)
[verb]
[bij-leg-gen, leg-de bij, bij-ge-legd]
When there is a deficit you will have to "bijleggen" 🙂 It is sometimes also used when you are losing money on a deal (e.g. offering somebody a very good (financial) deal, but having to invest money to make it happen).
Examples:
– "Jongens, er ligt niet voldoende geld op tafel om de rekening te voldoen, hup, iedereen 5 euro bijleggen!"
("Guys, there is not enough money on the table to settle the bill, come on, everybody contribute (another) 5 euro!")
– "Uiteindelijk heb ik maar gewoon een tientje bijgelegd om van het gezeik af te zijn!"
("Eventually I (just) put in a tenner more in order to be done with all the fuss!")
– "Ik moest van Den Haag naar Amsterdam rijden om m'n stereo te verkopen. Ja, dan moet ik erop bijleggen, ik ben gekke Henkie niet!"
("I was supposed to drive from The Hague to Amsterdam in order to sell my stereo. Right, that way I'll lose money on it, I'm not stupid!!" In this example you may also hear "toeleggen" instead of "bijleggen".)
Related words:
– Tekort: deficit [noun] [het tekort, de tekorten].
– Aanvullen: to supplement, to complete [verb] [vulde aan, aangevuld].
– Rekening: bill, check [noun] [de rekening, de rekeningen].