Android running slowly?
Lag time?
Glitches?
Force closes?
Slow?
The first thing to do is to do a simple Google search on the problem.
I promise you: you are not the first person to encounter this problem.
Actually, the first thing to do is turn it off and then on again.
Then try taking the battery out and putting it back in.
Then try reformatting the memory. (i.e. restore factory settings, this will delete all your personal information)
Here are some common complaints and how to fix them:
Glitches/slow:
Task Killers are great tools, but overused. A Task Killer can sit on your phone and slap down anything that tries to run in the background. Unfortunately, a lot of applications need to run in the background, in order to do the cool things you downloaded them for.
Even worse, every time you kill a system process, it needs to be rerun, which consume precious battery and speed.
A task killer should never be set to auto-kill but can be useful to close down manually any processes that start freaking out.
Battery Performance:
A handset with Bluetooth, GPS, NFC, Wi-Fi and screen on will run itself down in a few hours.
The worst of these, by an huge margin, is the screen.
You can get applications like Toggle Settings Lite that will turn down any of these features based on particular system states (e.g. turn Wi-Fi back on when you arrive home or turn screen to 'dim' after 8pm) but the screen use will still kill your battery in a very short time.
The simplest solution is to carry a data/recharge cable with you ($1 ebay) but you can also find many battery utilities on the web that will help you.
Some handsets, like the HTC Desire HD, have poorly calibrated batteries, and there are official fixes for this. Check out the manufacturer's website.
Lag:
To get more out of my Samsung Galaxy I gained root access (WARNING: WILL VOID YOUR WARRANTY AND POSSIBLY BREAK YOUR PHONE) and installed a new 'Rom' or 'Mod' on it. This just means instead of running the operating system that Samsung installed on it at the factory, I found a modified one on the web that I liked and installed that.
These are usually based on the manufacturer's designs, but are tweaked to remove branding, to increase streamlining, and to run faster.
Sounds hard, but if your handset is laggy it is worth considering.
If the mod you install is still glitchy - no problem: Just install another.
You can use RomManager to easily install and backup different mods.