Although I run a predominantly pre-4e game, I have adopted the 4th edition skills over the 3rd edition skills. They are more concise and seem to me to work more smoothly.
In 4e, each class had its own list of skills a character could select from and each character could train in a set number of skills from their list. The number they could train in varied by class. Some classes were automatically trained in one or more skills. Other classes were not. If you were trained in a skill you gained +5 on skill checks with that skill.
Instead of restricting skill choices by class, I decided to open up skill training to all skills for all classes. Each class has one prerequisite skill. The overall amount of skill training is now the same across the board. Since each trained skill counted as five plusses, I determined an average number of trained skills and multiplied that by five to determine skill points now available to all characters. Each skill point assigned to a skill now counts as +1 per point for skill checks using that skill.
Skills and Classes
Characters do not automatically learn any skills, nor do they inherit any restrictions on what skills they may learn, based on their class. Each class has a skill requirement though. Characters must have five points in the requisite skill to train in a class. The requisite skills are: Athletics for Fighters, Religion for Clerics, Thievery for Rogues, and Arcana for Wizards.
At first level each character has a set number of skill points (25 for Humans, 20 for other races). Five points must be spent in the requisite skill. No more than five points may be spent in any skill at this point.
At each level thereafter, the character gains one skill point that may be assigned to any skill.
After first level, up to ten skill points may be assigned to a single skill.
If you plan on training in multiple classes, it is necessary to plan ahead by assigning skill points to the skills required to train in those additional classes.
I renamed the Healing skill to First Aid. A skill check can be made as before to bind wounds and stop a dying character from taking any further damage. Dying characters (characters with zero or fewer hit points) take one point of damage every round (plus damage from any effects on them that give on-going damage) until they reach -10 hit points, at which point they are dead.
I added the Alchemy skill. This is more of a familiarity with alchemical ingredients that lets characters roll an Alchemy check to determine if they know if any part of a particular animal or monster, or a nearby vegetation or mineral, is of value to an alchemist. Furthermore, some ingredients must be collected in a certain way to avoid damaging them. The Alchemy skill allows the character a skill check to attempt to collect and package ingredients that require special care.