Wedding abroad is a trend that has led recently to a true tour operator business around it, but when it comes to expatriates this is run of the mill story.
You relocate abroad for job reason and en-route you also fell in love and want to get married.
Happy ending?

Not quite. As a matter of fact it is a straight recipe for chaos. In fact you may end up dealing with not just one jurisdiction, but two, when not even three (your home country, your country of residence, the home country of your spouse-to-be).
In most countries the marriage abroad is legally recognized if you are both free to marry and you have fulfilled all the legal requirements of the country in which you choose to marry, but do not overlook the fact that, although you must meet the foreign requirements for formalities, you are still bound by your country law as far as the capacity to marry is concerned (legal age of marriage is different in different countries).
Your foreign marriage certificate should usually be accepted for official purposes in your country of origin where you need to show evidence that you are married. If the certificate is in a foreign language, you must provide an official translation or a translation from a recognized translation agency.

You are now happily and legally married and you wish to bring your foreign national spouse home, right? Well, think again.
Dual citizenship as a result of marriage is it not as straightforward as you might think.  In fact, many governments have legislations to prevent marriages of convenience which result in tight measures when issuing entry permit, a visa or a residence permit to a foreign national spouse.
Don't expect that your foreign national spouse can automatically get your own country's citizenship or viceversa. For example, the american government will not automatically provide a foreign spouse with a USA visa, or even entry. The spouse who is the american national has to start immigration procedures for the foreign spouse by filing a petition and wait to receive approval prior to entry the country with the partner. 

What does it take to get married in another country?

First of all you need to make sure to meet all the legal requirements of the country you are marrying in. You should contact the relevant embassy or the religious authorities in that country to find out what is required.
You should realize that the legal validity of your marriage is governed, in part, by the laws of the country in which you  marry. In most, if not all cases, the legal formalities abroad are very different to those in your home country. For example, a church marriage abroad is usually a purely religious ceremony with no legal effect and since it is not recognized in law in the country in which it takes place, it cannot be regarded as a legal marriage in any other country.
But there are exceptions to this and countries like Israel will acknowledge only religious marriage ceremonies, while Switzerland and Japan will validate only civil ones.
In most countries the marriage abroad is legally recognized if you are both free to marry and you have fulfilled all the legal requirements of the country in which you choose to marry.

And here is the catch... the legal requirements of different countries are many and various, up to the point that they can be different even from state to state as is the case of  the USA. In Bali, there is a long list of formalities you will  need to satisfy before saying "I do", including proof that both partners belong to the same religion (it does not matter “which” religion), where New York, your passport a second proof of identity (driving license or ID) and one working day before the planned wedding in order to obtain a license is all is needed. 
This effectively means that anyone who has lost touch with a parent, anyone who has not been baptized or confirmed and couples of different religions cannot legally marry in Bali. In addition, the authorities require photographs of a particular size not commonly available outside Indonesia.
Other countries require you to complete medical tests. In Mexico, for example, you are required to take an HIV test and in Mauritius and Thailand, a woman who remarries within eight months or ten months of her decree absolute coming through will be required to have a pregnancy test or should present a declaration of not being pregnant.
Most countries have rules about residency before you can get married, from a few days to 40.
Normally you will require formal proof that you are free to marry and based on the country the marriage takes place in you may be required to abide some or all of the following:

• a period of residency in the country
• proof of  single status or certificate of "non-impediment to marriage" by both partners (You may require a Certificate of Freedom to Marry to get married in some foreign countries. This may also be called  "Certificate de Coutume" or "Certificate of Nulla Osta)
• birth certificates (quite often it is required that the birth certificate contains the full name of both parents
• blood test  results
• passports
• a secon proof of identity (driving license, ID)
• proof of divorce if either of the partners had been previously married
• if widowed certificate of marriage and certificate of death of the spouse
• parental consent  if a partner is not of marriage age or a court exempt order if the country of origin requires so. In fact, although you must meet the foreign requirements for formalities, you are still bound by your country law as far as the capacity to marry is concerned. For example, your marriage abroad will not be recognized in Ireland if you are marrying underage without a court exempting order.
  Most countries will require official translations and notarization of the documents.

Tour operator may be able to advise you on wedding abroad, but it would be better to get the information directly from the government through either the consulate or embassy of the country you are going to get married in.
Oh, last but not least, before embarking in this adventure, you might wish to enquire what are the consequences of a divorce abroad!