Take an easy track that you know well and record yourself singing it. Play it back and listen to the sounds to get an idea of the strengths and weaknesses of your voice. Repeat again but this time make notes of areas where you went wrong and make a list of things to work on.
Listen to different notes and chords with your eyes closed and build up your recognition of different sounds. Very few people are born with a natural instinct for the sounds, so the more you practice identifying the notes, the easier it will be to match the right notes when you sing.
Control your breathing by resting in between the notes and breathing deeply from your stomach instead of your chest. This is something that many people have to learn to do and will only come with practice. Put your hands on your upper stomach and back to feel the inhalations and better control your breath.
Attend a voice workshop or a singing class in your local area. This is cheaper than an individual lesson and it will give you an idea if the class is right for you. Take notes of the information and practice any exercises at home.
Make good song choices that compliment your voice and your stage of progress. Nasal low voices sound good with country music and high voices can carry a folk ballad. Very few people can sing Whitney Houston so start out with lower songs that are more level.
Master the basics such as your pitch recognition and note and chord matches before you insert vocal ornamentation such as slides into your songs. This is a different skill altogether and could throw off your initial progress.