Kissing can be very intimate, but for some they simply do not enjoy French kissing (kissing with tongues). If you are used to kissing with tongues, this can be very startling and shocking for you, so figuring out just how to kiss your partner, without using your tongue, can be a challenge.
Talking about it first is important. Your partner may feel that kissing without tongues feels better to them, or they may not enjoy the feeling of another person's tongue in their mouth. Whatever their reason, it is their choice, and trying to force them into using tongue will just ruin the mood completely. If they tell you they will only do kissing without tongues, accept it and go for it. You showing that you are perfectly happy with the arrange will help your partner to relax, guaranteeing you a better time than you would have had if you'd pushed.
For some, kissing with tongues is the ultimate kiss of passion, but you can be just as passionate without tongues. Start with light kisses on your partner's lips, slowly and gently, before using more pressure as time goes on. While they might not enjoy kissing with tongues, they may enjoy you gently sliding your tongue along their lip as you kiss.
Try lightly sucking on their lip, or even nibbling on it, as the kiss deepens. Keep experimenting with different things and see what they like best. More often then not, they will show you what they like by doing the same to you, so copying their movements can be a great help to you. Try not to let the worry take over, as kisses can be far better if you just get lost in the moment.