Having had some personal experience with the velib' system, I am going to explain how it works and pretty much why I prefer having my own bike.
The Velib' system is theoretically very easy..... but here are a few practical examples based only on my experience of what has happened
All you need is your credit card. After you conveniently find your nearest velib' station, follow the easy instructions and for the minimal cost of €1.70 a day or €8 a week (recently increased from €1 a day and €5 a week) you have access to the thousands of bikes located all over Paris.
After trawling to 3 different velib stations you finally find a velib' that has not been so damaged that it still can be technically counted as functional.
After trying to follow the confusing instructions at the podium you switch between a touch screen and a keypad for codes for 5-10 minutes. Two attempts will be necessary if this is your first time.
If you get this far this is good as sometimes the computer seems to freeze up at the terms and conditions part making it necessary to located another station with a functioning podium.
The cost of a velib' is only €1.70 per day or €8 per week, unless you are using the velib' for longer than 30 minutes at a time, in which case you will be charged €1 for the second half hour, €2 for the third, €4 for each subsequent half hour. 3 hours would therefore cost €15. Ouch.
While it is true that there are thousands of velibs around Paris, it is worth mentioning their most popular usage patterns, these can result in an inconvenient "velib rush hour" situation.
When I was living near the top of a hill at Anvers there were rarely any velib's available as most people would only take the bicycles to cycle down hill and not up, more than once this resulted on walking for 20 minutes to find a bike since all the surrounding stations were also empty, or the remaining bikes were damaged beyond use.
When finally locating a velib' and managing to use it to cycle to our central destination of Chatlet there were not any parking spaces available and after trying 3 different stations there I found one a 15 minute walk away from the bar where I was meeting friends.
1 hour velib' trip instead of a 25 min metro and 20 minute cycle.
However it is worth noting that some people really enjoy the system and find it very practical in their day to day life.