There *is* a skill tree - it's just not that obvious how to use it.
The skills label on your 'character sheet' doesn't appear to be used, however, if you look at the sklill tab (use <Alt-T> as mentioned above), you see the skills tree.
There in the top right you see what skill points you have ammassed, and you can then use the '+' on the various skill icons in the various tabs to increase that particular skill.
When you select to use the skills tree, you can't make items or use them if their skill level (shown on the item's tooltip in yellow) is above the skill level mentioned on the tooltip on the relevant icon in the skill tree (and it's not always obvious to me which is relevant!).
This means that at the beginning of the game you can only use (and make) the simplest of wooden tools.
Having played an adventure session with this feature enabled, I personally feel that it is more suited to a co-operative multi-player game than to a single-player game.
I don't think I'll try using it again until I'm very much more proficient in the adventure mode (if at all).