First, anything is better than dial up.
Look in your yellow pages for internet services. There may be several DSL providers, all of which go through the same phone wire to get to your home but some may be either faster or cheaper than others. Why that's possible is a long boring story. Most cities have just one cable provider, but a few cities have two. You just need to check around and see what's available and what you are willing to pay.
Any high speed service will probably cost more than you are paying for dial up, but trust me it's worth it. Once you have used any high speed service of any kind, using dial up is painful.
You need to be very careful about using mobile phone service for internet access, it all depends on their data plans. I've heard some real horror stories about outrageous bills when the user didn't check on the fine print.
And your wireless card was probably meant to be used with a local wireless router, not a wireless ISP.