Storage
Yes the toolshed is where you're meant to keep tools, but you aren't meant to just chuck them in there. For one, you'll never find them when you need them, and secondly, who knows how damaged they'll get from being knocked about and incorrectly stored? Not to mention problems like rust and decay if they're left unattended for long enough. You should store your tools in a way that is easy to search through and preferably organised by job (gardening together, hammer and nails, screws and screwdrivers) -- that way you'll never lose anything.

Cleaning
Yes, you've gotta clean your tools. Like knives and forks in the kitchen, each time you use a tool (especially a garden tool) make sure you give it a wipe down before you put it away. If you don't, you'll find they will quickly start to rust and decay, and may even stop working, this is especially true of precision tools like secateurs. Clean away all dirt and sap or other detritus, and give metal surfaces a wipe-over with an oiled rag to protect them.

Maintenance
Every now and then (even if you haven't used them) make sure you get your tools out, give them a clean and check them for rust, or oil up any moving parts. Look for broken or missing parts and accessories at the same time. Reunite parts that have become separated, or buy replacements if needed. Sharpen blades on spades and shovels, and put a new edge on your cutting tools. If the secateurs are too far gone, you can buy replacement blades for most models. By maintaining your tools this way, they will always be ready to go and you'll never be left stranded again.

Tip
It pays to keep extra bits (saw blades, screws, nails) on hand as you will never know when you might need them. If you do, make sure you keep them in a single spot and in their packaging so that they will always be ready to go should you need them.