How to know that your backlink was indexed by Google?

If you know the URL of your backlink, you could use the query

Site:URL in Google, and see if there is any record of it.

Check it on Backlinks Checker Tool - Backlink Watch . You can see all your backlinks there.

For people who do not know what a backlink is, in a nutshell it is a link that is on an external website and that points back to your own website. A backlink is basically a vote from one site to another. The more backlinks that we get pointing back to our websites, the higher we will rank in the search engines. The higher the rank, the more traffic and sales we'll make.
That is the short version. What many people forget about though is if they get a backlink on a specific page within a website and that page is not in Google's index the backlink will not be valid and will therefore not help your rankings. Why? Because if Google doesn't know about that page, it won't know about your backlink within that page.
What we need to do is ensure that all the pages that include a backlink to our website are indexed in Google. There are many ways of doing this. All we need to do is help Google find these pages so that it can crawl and cache them adding our backlinks to their links database.
Many people ask why we need to do this. The answer is simple. Although the search engines have many powerful servers running different tasks on an ongoing basis it still has to process and monitor billions of web pages. If a website adds new pages on a regular basis, even with the use of a sitemap it is easy for some of those pages to get buried which makes it harder for the search engines to find them.
So how do we get these pages indexed. Although the timescale can vary, the concept is quite simple. We use various types of sites such as popular bookmarking sites and forums as the search engine bots will frequent those sites almost constantly. All we do is link to our 'backlink pages'. With bookmarking sites you would simply bookmark the urls and with forums you would temporarily add a link to your forum signature which would instantly populate potentially hundreds of indexed forum threads with the link. Using methods like this you can often get your backlinks indexed in a matte of hours.

you can check your backlink by search in Google "site:yourdomainname.com

Or

There are many tools available to check backlinks you can try backlinkwatch.com

SEOSpyglass is another useful tool, when it comes to checking backlinks...

There are various tool available for that where just putting your url you will get to know the whole list of backlinks. I generally make use of backlinkwatch to check the list of backlinks getting to my site.