If you were married overseas.. meaning not in Thailand.. then the first step is to get a copy of the original marriage certificate certified by the Embassy (or sometimes it's a service performed by the Consulate) of the country where your marriage took place.. for most people that's likely to be their home country.. so you may be able to do this before you leave for Thailand.. however, you could have had a vacation style wedding of course, which would need to involve a foreign Embassy in the process.. but if you are already in Thailand then things are slightly different.. first step, your overseas marriage certificate has to be authenticated by the relevant country Embassy in Bangkok before you can move on to the second step.. which is getting a copy of the original (now already Embassy certified) marriage certificate translated into Thai and getting the translated copy certified by the Ministry of Foreign Affairs (also in Bangkok) .. only then will you have the correct documents to be able to register your marriage at your local Amphur in Thailand.. which is necessary to obtain a Kor Ror 22 (another certificate) from them.. which is a document you will need to support your non-o married visa application at Immigration.. given the complexities and inconvenience involved in this process I'd say it's probably best to engage an agent who knows the ropes and can expedite this for you.. we are in CM and didn't want to waste our time and energy traveling to Bangkok in person.. so we found an agent that specialises in translation services that could do everything for us and produce the certified marriage documents.. this process took them around 2
***
weeks from start to finish and we agreed to attend the final document collection at the International Convention Center in CM to reduce the wait by a few days.. otherwise it would have been a 3-week wait.. the fee was just over 5,000 baht in total.. and they threw in a translated copy of my passport for good measure.. which wasn't needed by the Amphur to register the marriage but i guess it might come in useful later.. be aware that your Amphur may try to retain the original certified copies instead of simply taking copies of them for their records.. which is outrageous imo since you may need to use them elsewhere in the future.. and you won't want to have to repeat this exercise and incur further unnecessary expense.. i pushed back hard and told our Amphur they could only keep them if they gave me a legal undertaking to return them if i needed them.. or alternatively, agreed to pay an agent the necessary fee to produce another set for me.. and after deliberation and consultation with superiors they backed down and simply took copies which they had us certify as genuine copies!
Ps. It appears that you have already attended to the certification of the native marriage certificate.. therefore you are ready to move on to the translation and certification by the MoFA in Thailand.. though it may be worth checking if you can get this done at the Thai Embassy in the Netherlands.. so it's all done before you travel to Thailand.. however if you are already in country then a translation agent is your best option.
PPS. And note, the local Amphur and the Municipality are 2 different authorities within a district.. and are often housed in different buildings.. marriage registration is handled at the Amphur.. as was my Pink ID card application.. whereas Yellow books are the domain of the Municipality.. as is stuff like refuse collection and street lighting etc 😉