Tickets go on sale at different times of year. I think tickets for this year haven’t gone on sale yet (but that’s probably because the organisers are waiting to be sure how many people they can have in the venue with Covid).
Before Covid, they often went on sale around November to January. You can sign up on the Eurovision website to receive email alerts. You can also join fan groups on Facebook or follow fan blogs on Twitter etc - they will usually be buzzing as soon as a ticket sale date is confirmed.
Be prepared for a very competitive effort to get tickets. Treat it as you would any other concert you know will sell out in a matter of minutes.
Also, decide which show you want tickets for. You can get tickets for any of the live shows - the Semi finals on Tuesday and Thursday, or the Final on Saturday. The tickets for the Saturday night show are obviously like gold dust. You can also get tickets for the rehearsal shows - usually a day time ‘family’ rehearsal (good with kids, the easiest to find tickets for and the one a lot of locals will go to) or the jury rehearsal which is the night before the actual live show. Rehearsals are great shows to get to - tickets are easier to come by (and cheaper) but still loads of fun. I actually prefer going to the Friday night jury rehearsal than the Saturday night live show.
Also decide where you want to sit or stand. The organisers will often release the layout and ticket price bands before they go on sale. This is a matter of preference - I’ve had more fun standing (or rather dancing) but sometimes these can be restricted to registered fans or people getting tickets through fan club packages. If you’re sitting, tailor your seat if you can to whether you want to be up and dancing in your seat or prefer to sit and watch.
Hotels and accommodation books up QUICKLY, especially if it’s hosted in a relatively small city. Dates are usually provisionally in place well in advance and most countries usually only have a choice of three or four realistic host cities. So you might want to book a free cancellation hotel for the possible host cities on the most likely date. That way, once dates and cities are confirmed, you’re in ahead of the game and don’t have to compete with everyone rushing to book once city is confirmed.
To get the most of the experience, join fan groups to find out the best places to hang out while you’re there. You can find out the best places to watch the shows you’re not attending (they’re often shown in public squares in the host city). You can also find out the details of getting access to the official nightclub or the fan nightclub - arrangements vary from year to year but these offer great places to dance the nights away and often you’ll be hanging out near the participating artists. They often have live performances etc. lots of fun. Sometimes anyone can buy a ticket for entry, sometimes only registered fans can, sometimes it’s entirely restricted to the delegations.
The main thing for me is always making it a real Eurovision trip. Enjoying Eurovision music in bars and clubs, hanging out with other fans etc. its much more than just the show you go to. So even if you didn’t get tickets you could also consider just hanging out in the host city for a few days to soak up the atmosphere.