###Flow

The concept you're looking for is called flow. When in a flow state, you enter a sort of trance where the game's challenges feel "right," you're "in the zone," etc.

###Anxiety

As you've noted, anxiety will kill your flow:

Some of the challenges to staying in flow include states of apathy, boredom, and anxiety. [...] Lastly, a state of anxiety occurs when challenges are so high that they exceed one’s perceived skill level causing one great distress and uneasiness.

Part of what the Wikipedia article is talking about is anxiety due to the game being too challenging for your current skill level. Thus, one solution is to reduce the challenge level or increase your skill level.

###Increased Skill/Decreased Challenge

In a rhythm game, you might practice the section of the song that is giving you trouble. Playing on a lower difficulty level might also give you more practice, letting you build your skill.

###Building Confidence

Of course, part of this too is confidence. If you don't have confidence in your skill, you'll be anxious as you worry that you're going to fail. One thing I do to renew my confidence is recall my gaming history. There have been many times when I've overcome impossible odds in a game, or made epic plays. Trying to remember those times can reassure you of your skill, boosting your confidence.

###Anxiety & Health

Anxiety is also related to your health. What you eat and drink, what medications you're on, etc. Caffeine and other stimulants can make you anxious, depending on your intake. There are also various medicinal and herbal ways to reduce anxiety - some people enjoy herbal tea, for instance.

Physical activity has also been shown to reduce anxiety. Try taking a short walk - even a 10 minute walk has been shown to significantly reduce anxiety.

###Dealing With It

Despite all this preparation, in the moment, anxiety is still going to creep up and make you feel stressed out. Deep, slow breathing and relaxing your fingers can help to control it.

Flow

The concept you're looking for is called flow. When in a flow state, you enter a sort of trance where the game's challenges feel "right," you're "in the zone," etc.

Anxiety

As you've noted, anxiety will kill your flow:

Some of the challenges to staying in flow include states of apathy, boredom, and anxiety. [...] Lastly, a state of anxiety occurs when challenges are so high that they exceed one’s perceived skill level causing one great distress and uneasiness.

Part of what the Wikipedia article is talking about is anxiety due to the game being too challenging for your current skill level. Thus, one solution is to reduce the challenge level or increase your skill level.

Increased Skill/Decreased Challenge

In a rhythm game, you might practice the section of the song that is giving you trouble. Playing on a lower difficulty level might also give you more practice, letting you build your skill.

Building Confidence

Of course, part of this too is confidence. If you don't have confidence in your skill, you'll be anxious as you worry that you're going to fail. One thing I do to renew my confidence is recall my gaming history. There have been many times when I've overcome impossible odds in a game, or made epic plays. Trying to remember those times can reassure you of your skill, boosting your confidence.

Anxiety & Health

Anxiety is also related to your health. What you eat and drink, what medications you're on, etc. Caffeine and other stimulants can make you anxious, depending on your intake. There are also various medicinal and herbal ways to reduce anxiety - some people enjoy herbal tea, for instance.

Physical activity has also been shown to reduce anxiety. Try taking a short walk - even a 10 minute walk has been shown to significantly reduce anxiety.

Dealing With It

Despite all this preparation, in the moment, anxiety is still going to creep up and make you feel stressed out. Deep, slow breathing and relaxing your fingers can help to control it.