Penance for Lent.

What does it consist of?
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Many people other than Catholics give up stuff for Lent.  Some of those who are Catholic, often do not really practice the faith otherwise, but they like to do something for Lent.  Frequently they give up sweets or some other enjoyment.  That's cool.  But penance doesn't mean much - or rather count for much - if you don't try to give up sin or keep the Commandments.  No matter how nice we are, we have to keep the Commandments - not just the big 10, but the commandments of the Church as well.  So the best penance for people who hold onto particular sins is to give up sin.  Just think, your entire Lent could consist in not doing that thing you love to do.  (Although if you can't give up sin, then keep giving up the sweets and keep praying - at least it's a start.  Don't forget to ask for the grace to give up sin, or even the grace to want to ask for the grace to give it up.)
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For us ordinary sinners, frequenting the sacrament of penance is a very good Lenten discipline.  Praying more and doing more spiritual reading is good too.  The idea of giving something up makes more sense when you do it as a voluntary discipline and as a way to make time for God through more prayer, reading, and/or good works.  For instance, if you like to drink and watch TV, skip the drink and turn off TV to do something edifying or charitable.  If that is too hard, have the drink and do your spiritual reading instead of watching TV.  Stuff like that.  (I just said that for you know who.)
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The Church prescribes definite penances for us, Friday abstinence, Ash Wednesday and Good Friday fasting, etc. - if you observe them faithfully and add some extra personal sacrifice, that is a good observance of Lent for a lay person with the daily obligations of a job, a family, a mental problem like Charlie, keeping cats, or something else.  Our Lord revealed to Sr. Lucia of Fatima that the penance he exacts and demands of people today is fidelity to the duties of their state in life.  Imagine if we just resolved to do that for Lent?  Don't call in sick.  Don't pretend there is static on the line and later tell Cathy you must have been cut off on the phone.  Don't skip your morning and evening prayers to check your email.  Don't skip paying a bill when you would be able to pay it if you didn't buy this or that.  The faithful fulfillment of our daily duties is a great penance.  For those of us who sometimes imagine we don't have sins and imperfections  we are actually attached to, doing our daily duty may surprise us.  Looking back on my life, I could go to hell just for all of the times I completely avoided my daily duty.  Seriously.
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Our Lady also indicated appropriate penances to the Fatima children, as well as to Sr. Agnes of Akita.  She asked them if they would accept all the suffering that came their way as a sacrifice and a penance - in addition to the fulfillment of their daily duties, little mortifications and daily prayers.  See how simple that is?  For instance, if a person is sick or disabled - they already have a sort of built in penance. 
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Monastics, such as the Russian Archbishop I'm reading, as well as St. Therese of Lisieux, all speak of little observances.  The Archbishop recommends the novices never eat to satiety - that is, leave the table a little hungry - but eat according to your custom.  Therese says to bear patiently the little annoyances we encounter during the day, from one another or by circumstance.  She even suggests we offer our failures and humiliations as a sacrifice - trusting in God's mercy and love.  Little Therese would also most likely recommend we not complain so much about how hard it is, or how dry the desert is, or how severe the temptations are.  Remember what Jesus said to those types, "What did you go out to the desert to see?  A reed swaying in the wind?  A man dressed in fine clothes?"
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I very much like what Tara's priest (I think it is Fr. Eric) had to say on the subject - in Tara's words:  "Father said that penance is not something we take on to make ourselves miserable--as if God wanted us to suffer--contrary--penance is as a "spiritual exercise," and in much the same way, if one started to exercise a weak flabby body--with it's impending soreness--the soreness or suffering is just a by product of the good exercise. And so we take on good "spiritual exercises" during Lent." - Loved Sinner 
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Keep it simple.  And if you fail - offer it up and try again.  Lent isn't a competition or a reality TV show like The Biggest Loser.
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Disclaimer:  Don't listen to me - I'm only sharing things that have helped me along the way.  Always check with your priest/confessor for sound teaching and clear instruction.

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Photo:  Los Penitentes, New Mexico  (Don't do this at home.)