The problem lies with connotation (feeling or mood associated with words). Giggle has a happy or slightly negative connotation and is associated with young girls and women laughing. Snigger has a very negative mood and suggests a sense of being better than the person you're laughing at. Smirk is different from the others because it isn't a laugh. It means smile, but the connotation is negative because the person who is smirking things they are smarter or better than the other person/people in the room. I don't know the words titter and guffaw and I'm a well educated native speaker. I suggest you start using a good learner's dictionary, like the Oxford Advanced Learner's Dictionary, which explains the differences between words like this. Here is a link to the free online version (note that having the real book is better): http://www.oxfordlearnersdictionaries.com/

Another tip is to use an image search for each word. Still, be aware that you may get some odd results if there's a pop-culture reference (eg. bands, TV series, celebrities, etc)... turns out that "Titter" is also the name of an old pin-up mag.