Automation Testing Vs Manual Testing

One can know when to automate and when to manually test using common sense which has always been the general thumb rule especially when one has to come up with deterministic set of guidelines on how & when to automate. If one has to run the test once or twice and the test's really very costly to automation, it's most likely a manual test.

Manual Testing in which testers' tests software in order to find defects and also testers play the roles of end users. Manual Testing tester performs all testing operations in all the phases of the STLC being tested by human efforts.
Some important aspects to be considered in Manual Testing: 

Manual testing costs less than automation testing. If the test case only runs two times a coding milestone most likely it should be a manual test. It allows the tester to perform more random testing.
The more time a tester spends playing with the feature the greater of finding real bugs. Manual testing is very time consuming as it's done manually. If there is a new build, each time the tester must rerun all required tests.
Automation testing testers use some automated tools to test the software. It is performed where the user operations of the application are performed automatically by running some scripts using automated tools. In case of testing large software or executing a huge number of test cases automation testing is preferable.
While performing Automation testing some important aspects to be considered: 

To run a set of repeated tests, automation is preferable. Automation testing provides the ability to run automation against code that frequently changes & in mainstream scenarios to catch regressions in a timely manner. It also aids in testing a large test matrix. On different machines the automated tests can be run at the same time, whereas the manual tests have to be run sequentially.
As automation testing is very expensive than running the test manually. Visual references cannot be automated, for e.g. just via code or the automation tool it's not possible to tell the font colour, it is a manual test.
Some of the top challenges in testing are: 

Testing each & every application combination is an impossible task both in automation & manual testing. Tester requires good communication and analyzing skills to handle the relation very carefully with the developers in order to complete the work in a tester's way.
Regression testing work becomes complex when the project goes on expanding. Testing always under time constraint when the task has to be completed faster and which also includes writing, executing, automating and reviewing the test cases. It's very important to understand that which test has to be executed first.
Testers are responsible to find out the requirements of the customer for this they have to communicate properly to understand the requirements. The question of when to stop testing is difficult to answer since it requires core judgement of testing processes as well as importance of each of them.
As days are changing rapidly in application methods, reusing the test scripts will be very difficult to manage the test tools and test scripts. Testers only concentrate on finding easy bugs because of this there will be hard or subtle bugs will remain unnoticed.