Most of LogicMonitor's AWS Datasources are already configured to query the CloudWatch API. You can tell whether a datasource is collecting information from CloudWatch or not by looking at the Collector field in the datasource definition:

Once you've identified a DataSource and either cloned it or are ready to modify it, you'll need to identify a DataPoint to start from - you'll start from an existing DataPoint and modify it to collect the custom data you desire.  At the bottom of the datasource definition you'll see all of the datapoints (individual metrics) being collected. Click the manage gear icon for any normal datapoint and then click 'Clone' in the bottom right hand corner of the datapoint configuration dialog. Note that you need to clone a normal datapoint (cloning a complex datapoint won't work) - you can tell whether the datapoint is complex or normal by looking at the title of the datapoint configuration dialog:

The Metric path is what tells LogicMonitor which information to collect from CloudWatch.  The syntax for the Metric path is:

Namespace>Dimensions>Metric>AggregationMethod

where Dimensions should be one or more key value pairs in this format:

Dimensions = DimensionName1:DimensionValue1>DimensionName2:DimensionValue2

and so on and so forth.  Note that because spaces are allowed in CloudWatch metric names, white spaces in the metric path will be interpreted by LogicMonitor as a space in the specified name.  As such, you should avoid using white spaces where they aren't included in your CloudWatch metrics.  Additionally note that some metrics may not have an aggregation method, or may only expose certain aggregation methods.  The easiest way to ensure that you construct the metric path correctly is to use an AWS tool such as the AWS CLI to list-metrics.  After doing so, you can edit the Metric Path for a cloned or new datapoint like so:

The following example illustrates adding a datapoint to the AWS_Route53 datasource to monitor SSLHandshake Time.  While not a custom CloudWatch metric, this is a metric that was somewhat recently introduced by AWS (and as such will be added automatically to the AWS_Route53 datasource, but the process for editing / adding datapoints to AWS datasources is still illustrated).  First, a list-metrics with the AWS CLI displays the following:

Typically, issues arise because of the following:

1. Incorrect Metric Path Syntax.  Consider using a tool like the AWS CLI to confirm the syntax is correct.  
2. Incorrect Aggregation Method.  Is the aggregation method you are trying to use actually valid for the desired Metric?
3. Insufficient Permissions.  Sometimes, custom CloudWatch metrics can require permissions beyond what you may have provisioned to your LogicMonitor user.

You can identify which specific issue is occuring with the Poll Now functionality for your DataSource - you can find the Poll Now option on the Raw Data tab.  It'll display the request LogicMonitor makes to AWS for your DataSource, as well as any errors AWS returns.