For FamilySearch.org, which is the website referenced in the linked question, there are two types of accounts, one a free guest account which anyone can register for, and one an LDS account, which is for members of the LDS church.
For the records listed in the linked question, I am in the USA. I can see the extract from each record whether I am logged in with my non-LDS account or not. This may not be the case in other countries -- FamilySearch has to abide by the agreement they have with the record holders, and the privacy laws of each country. I cannot see the images themselves. Instead I get this message:
The easiest way around the problem is to go to a local FamilySearch center (a Family History Center or Family History Library) to view the images in-house. To find your local center: Find a Family History Center
However, your local center may be an hour away, or worse. What next? You can prepare for your research trip, or try to see if the records are available on another website. The advantages of preparing for a trip to the center, whether you need to visit one, or not, is that you'll have a record of what you plan to look for before you go, and a record of what you found, or didn't find, after you are done. FamilySearch has some excellent resources on creating a research log:
There are other ideas for getting ready to use FHL microfilms here on G&FH.SE too:
Another approach is to use a Genealogy Source Checklist. But whatever approach you use, go back to the place where you found your links and look carefully to see if you missed any clues about where the records are from. For our example, I can see the source citations and what films the images are from -- for one of the records listed, the information looks like this:
Once you have the title of the FamilySearch database that the records come from, you can look for the same information on other sites like Ancestry or MyHeritage. Put the title into Google or your favorite search engine and see what comes up. Check archives and libraries near you to see if they have their own indexes, finding aids, research guides, or other substitutes for the records, or if you can access the records at the archive or library. Whether you can see the original images or not, read the FamilySearch Wiki article about that collection of historical records: Nicaragua Civil Registration (FamilySearch Historical Records) so that you can see what information might be contained in the records -- you will want to know this before ordering films in to a local center or making a research trip to somewhere you can view them.
Also check the FamilySearch Wiki for a Record Selection Table for that country to see if there might be other sources that contain the information you are looking for. If you haven't already, look at the main article on the country (see Nicaragua Genealogy) and look for a blue button that says Online Records to go to the what records might be online.
You can also use the FamilySearch Catalog to do a place search or a subject search, then look to see what might be available in other libraries closer to you, using resources like WorldCat, ArchiveGrid, Google Books, Hathi Trust, and The Internet Archive.
Try sites like Cyndi's List, Linkpedia, and Wikipedia to find other sources of information or to get background information about the topic.
Your goal is to be prepared, so that when you do finally get access to the original images, you'll be better able to make use of the information that can be found inside. You don't want to spend a lot of time and money ordering film and extracting only part of the records, only to find out later that you should have also copied some of the other information (like the names of witnesses) while you had the chance.
To avoid getting into the same problem again later, try your best to write a good source citation so you know where the records came from and that you understand the nature of the records.
Worst case scenario: you have to pay someone to retrieve original copies for you. In that case, you'll want to have a good description of what you're looking for, so the other researcher knows exactly what you want.
Don't be afraid to use more than one website. I regularly check ALL the websites available to me when I'm looking at a records so I can understand what I'm looking at. Different sites present the information in different ways, and sometimes I have to combine information from several different sites to see what is really going on.